Daily Papers

Energy consumption in solving computational problems has been gaining growing attention as a part of the performance measures of computers. Quantum computation is known to offer advantages over classical computation in terms of various computational resources; however, its advantage in energy consumption has been challenging to analyze due to the lack of a theoretical foundation to relate the physical notion of energy and the computer-scientific notion of complexity for quantum computation with finite computational resources. To bridge this gap, we introduce a general framework for studying the energy consumption of quantum and classical computation based on a computational model that has been conventionally used for studying query complexity in computational complexity theory. With this framework, we derive an upper bound for the achievable energy consumption of quantum computation. We also develop techniques for proving a nonzero lower bound of energy consumption of classical computation based on the energy-conservation law and Landauer's principle. With these general bounds, we rigorously prove that quantum computation achieves an exponential energy-consumption advantage over classical computation for solving a specific computational problem, Simon's problem. Furthermore, we clarify how to demonstrate this energy-consumption advantage of quantum computation in an experimental setting. These results provide a fundamental framework and techniques to explore the physical meaning of quantum advantage in the query-complexity setting based on energy consumption, opening an alternative way to study the advantages of quantum computation.

The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is beyond the capability of any classical computer, an event known as quantum supremacy. This would be easier to achieve experimentally than full-scale quantum computing, but involves new theoretical challenges. Here we present the leading proposals to achieve quantum supremacy, and discuss how we can reliably compare the power of a classical computer to the power of a quantum computer.

Ridgelet transform has been a fundamental mathematical tool in the theoretical studies of neural networks. However, the practical applicability of ridgelet transform to conducting learning tasks was limited since its numerical implementation by conventional classical computation requires an exponential runtime exp(O(D)) as data dimension D increases. To address this problem, we develop a quantum ridgelet transform (QRT), which implements the ridgelet transform of a quantum state within a linear runtime O(D) of quantum computation. As an application, we also show that one can use QRT as a fundamental subroutine for quantum machine learning (QML) to efficiently find a sparse trainable subnetwork of large shallow wide neural networks without conducting large-scale optimization of the original network. This application discovers an efficient way in this regime to demonstrate the lottery ticket hypothesis on finding such a sparse trainable neural network. These results open an avenue of QML for accelerating learning tasks with commonly used classical neural networks.

We introduce fusion-based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.

In this paper, we propose the Quantum Data Center (QDC), an architecture combining Quantum Random Access Memory (QRAM) and quantum networks. We give a precise definition of QDC, and discuss its possible realizations and extensions. We discuss applications of QDC in quantum computation, quantum communication, and quantum sensing, with a primary focus on QDC for T-gate resources, QDC for multi-party private quantum communication, and QDC for distributed sensing through data compression. We show that QDC will provide efficient, private, and fast services as a future version of data centers.

Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (ibm\_fez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of approx0.37% and approx0.31%, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states |H_Lrangle and |T_Lrangle achieve fidelities of 0.8806pm0.0002 and 0.8665pm0.0003, respectively, which are both above the magic state distillation threshold. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as 0.8356pm0.0003. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.

The quantum advantage threshold determines when a quantum processing unit (QPU) is more efficient with respect to classical computing hardware in terms of algorithmic complexity. The "green" quantum advantage threshold - based on a comparison of energetic efficiency between the two - is going to play a fundamental role in the comparison between quantum and classical hardware. Indeed, its characterization would enable better decisions on energy-saving strategies, e.g. for distributing the workload in hybrid quantum-classical algorithms. Here, we show that the green quantum advantage threshold crucially depends on (i) the quality of the experimental quantum gates and (ii) the entanglement generated in the QPU. Indeed, for NISQ hardware and algorithms requiring a moderate amount of entanglement, a classical tensor network emulation can be more energy-efficient at equal final state fidelity than quantum computation. We compute the green quantum advantage threshold for a few paradigmatic examples in terms of algorithms and hardware platforms, and identify algorithms with a power-law decay of singular values of bipartitions - with power-law exponent alpha lesssim 1 - as the green quantum advantage threshold in the near future.

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable and fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional hybrid resource states comprising both bosonic qubits and squeezed vacuum states. The proposal enables exploiting state-of-the-art procedures for the non-deterministic generation of bosonic qubits combined with the strengths of continuous-variable quantum computation, namely the implementation of Clifford gates using easy-to-generate squeezed states. Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions. By reducing the experimental challenges as compared to existing architectures and by enabling room-temperature quantum computation, our design opens the door to scalable fabrication and operation, which may allow photonics to leap-frog other platforms on the path to a quantum computer with millions of qubits.

Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is still unknown, and their preparation can be highly costly in computational resources. In this paper, we show how to prepare a large class of CSS stabilizer states useful for FTQC. We propose distillation protocols using syndrome encoding by classical codes or quantum CSS codes. Along the same lines, we show that classical coding techniques can reduce the ancilla consumption in Steane syndrome extraction by using additional transversal controlled-NOT gates and classical computing power. In the scenario of a fixed ancilla consumption rate, we can increase the frequency of quantum error correction and effectively lower the error rate.

Kerr nonlinear oscillators driven by a two-photon process are promising systems to encode quantum information and to ensure a hardware-efficient scaling towards fault-tolerant quantum computation. In this paper, we show that an extra control parameter, the detuning of the two-photon drive with respect to the oscillator resonance, plays a crucial role in the properties of the defined qubit. At specific values of this detuning, we benefit from strong symmetries in the system, leading to multiple degeneracies in the spectrum of the effective confinement Hamiltonian. Overall, these degeneracies lead to a stronger suppression of bit-flip errors. We also study the combination of such Hamiltonian confinement with colored dissipation to suppress leakage outside of the bosonic code space. We show that the additional degeneracies allow us to perform fast and high-fidelity gates while preserving a strong suppression of bit-flip errors.

Quantum computation is an emerging technology with important potential for solving certain problems pivotal in various scientific and engineering disciplines. This paper introduces an efficient quantum protocol for the explicit construction of the block-encoding for an important class of Hamiltonians. Using the Schrodingerisation technique -- which converts non-conservative PDEs into conservative ones -- this particular class of Hamiltonians is shown to be sufficient for simulating any linear partial differential equations that have coefficients which are polynomial functions. The class of Hamiltonians consist of discretisations of polynomial products and sums of position and momentum operators. This construction is explicit and leverages minimal one- and two-qubit operations. The explicit construction of this block-encoding forms a fundamental building block for constructing the unitary evolution operator for this Hamiltonian. The proposed algorithm exhibits polynomial scaling with respect to the spatial partitioning size, suggesting an exponential speedup over classical finite-difference methods. This work provides an important foundation for building explicit and efficient quantum circuits for solving partial differential equations.

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their non-local encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a Two-Photon Exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it only induces a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat qubit experiments.

The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of non-perfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of non-local stabilizer operators of the target state (i.e., the GHZ state), where each non-local measurement consumes another (non-perfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.

We present a method to convert certain single photon sources into devices capable of emitting large strings of photonic cluster state in a controlled and pulsed "on demand" manner. Such sources would greatly reduce the resources required to achieve linear optical quantum computation. Standard spin errors, such as dephasing, are shown to affect only 1 or 2 of the emitted photons at a time. This allows for the use of standard fault tolerance techniques, and shows that the photonic machine gun can be fired for arbitrarily long times. Using realistic parameters for current quantum dot sources, we conclude high entangled-photon emission rates are achievable, with Pauli-error rates per photon of less than 0.2%. For quantum dot sources the method has the added advantage of alleviating the problematic issues of obtaining identical photons from independent, non-identical quantum dots, and of exciton dephasing.

The fundamental trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, many emerging quantum architectures are designed to achieve high coherence at the expense of having fixed spectra and consequently limited types of controllable interactions. Here, by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model is on one hand the basis for many-body quantum simulation of spin systems, and on the other hand the primitive for an expressive quantum gate set. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ, and SWAP gates with estimated fidelities of 99.32(3)%, 99.72(2)%, and 98.93(5)%, respectively. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate with a fidelity of 96.18(5)%. Importantly, the protocol is applicable to various fixed-frequency high-coherence platforms, thereby unlocking a suite of essential interactions for high-performance quantum information processing. From a broader perspective, our work provides compelling avenues for future exploration of quantum electrodynamics and optimal control using the Floquet framework.

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called nabla^2DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level (omegaB97X-D/def2-SVP) for each conformation. Moreover, nabla^2DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.

The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G = 2.27 pm 0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.

Code Large Language Models (Code LLMs) have emerged as powerful tools, revolutionizing the software development landscape by automating the coding process and reducing time and effort required to build applications. This paper focuses on training Code LLMs to specialize in the field of quantum computing. We begin by discussing the unique needs of quantum computing programming, which differ significantly from classical programming approaches or languages. A Code LLM specializing in quantum computing requires a foundational understanding of quantum computing and quantum information theory. However, the scarcity of available quantum code examples and the rapidly evolving field, which necessitates continuous dataset updates, present significant challenges. Moreover, we discuss our work on training Code LLMs to produce high-quality quantum code using the Qiskit library. This work includes an examination of the various aspects of the LLMs used for training and the specific training conditions, as well as the results obtained with our current models. To evaluate our models, we have developed a custom benchmark, similar to HumanEval, which includes a set of tests specifically designed for the field of quantum computing programming using Qiskit. Our findings indicate that our model outperforms existing state-of-the-art models in quantum computing tasks. We also provide examples of code suggestions, comparing our model to other relevant code LLMs. Finally, we introduce a discussion on the potential benefits of Code LLMs for quantum computing computational scientists, researchers, and practitioners. We also explore various features and future work that could be relevant in this context.

This article summarises the current status of classical communication networks and identifies some critical open research challenges that can only be solved by leveraging quantum technologies. By now, the main goal of quantum communication networks has been security. However, quantum networks can do more than just exchange secure keys or serve the needs of quantum computers. In fact, the scientific community is still investigating on the possible use cases/benefits that quantum communication networks can bring. Thus, this article aims at pointing out and clearly describing how quantum communication networks can enhance in-network distributed computing and reduce the overall end-to-end latency, beyond the intrinsic limits of classical technologies. Furthermore, we also explain how entanglement can reduce the communication complexity (overhead) that future classical virtualised networks will experience.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

In molecular research, simulation \& design of molecules are key areas with significant implications for drug development, material science, and other fields. Current classical computational power falls inadequate to simulate any more than small molecules, let alone protein chains on hundreds of peptide. Therefore these experiment are done physically in wet-lab, but it takes a lot of time \& not possible to examine every molecule due to the size of the search area, tens of billions of dollars are spent every year in these research experiments. Molecule simulation \& design has lately advanced significantly by machine learning models, A fresh perspective on the issue of chemical synthesis is provided by deep generative models for graph-structured data. By optimising differentiable models that produce molecular graphs directly, it is feasible to avoid costly search techniques in the discrete and huge space of chemical structures. But these models also suffer from computational limitations when dimensions become huge and consume huge amount of resources. Quantum Generative machine learning in recent years have shown some empirical results promising significant advantages over classical counterparts.

Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective quantum feature maps for real-world datasets, particularly in the absence of sufficient prior information, remains a significant obstacle. In this study, we present a data-driven approach that automates the design of problem-specific quantum feature maps. Our approach leverages feature-selection techniques to handle high-dimensional data on near-term quantum machines with limited qubits, and incorporates a deep neural predictor to efficiently evaluate the performance of various candidate quantum kernels. Through extensive numerical simulations on different datasets, we demonstrate the superiority of our proposal over prior methods, especially for the capability of eliminating the kernel concentration issue and identifying the feature map with prediction advantages. Our work not only unlocks the potential of quantum kernels for enhancing real-world tasks but also highlights the substantial role of deep learning in advancing quantum machine learning.

Molecular docking is an important tool for structure-based drug design, accelerating the efficiency of drug development. Complex and dynamic binding processes between proteins and small molecules require searching and sampling over a wide spatial range. Traditional docking by searching for possible binding sites and conformations is computationally complex and results poorly under blind docking. Quantum-inspired algorithms combining quantum properties and annealing show great advantages in solving combinatorial optimization problems. Inspired by this, we achieve an improved in blind docking by using quantum-inspired combined with gradients learned by deep learning in the encoded molecular space. Numerical simulation shows that our method outperforms traditional docking algorithms and deep learning-based algorithms over 10\%. Compared to the current state-of-the-art deep learning-based docking algorithm DiffDock, the success rate of Top-1 (RMSD<2) achieves an improvement from 33\% to 35\% in our same setup. In particular, a 6\% improvement is realized in the high-precision region(RMSD<1) on molecules data unseen in DiffDock, which demonstrates the well-generalized of our method.

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

Breakthroughs in machine learning (ML) and advances in quantum computing (QC) drive the interdisciplinary field of quantum machine learning to new levels. However, due to the susceptibility of ML models to adversarial attacks, practical use raises safety-critical concerns. Existing Randomized Smoothing (RS) certification methods for classical machine learning models are computationally intensive. In this paper, we propose the combination of QC and the concept of discrete randomized smoothing to speed up the stochastic certification of ML models for discrete data. We show how to encode all the perturbations of the input binary data in superposition and use Quantum Amplitude Estimation (QAE) to obtain a quadratic reduction in the number of calls to the model that are required compared to traditional randomized smoothing techniques. In addition, we propose a new binary threat model to allow for an extensive evaluation of our approach on images, graphs, and text.

In the emergent realm of quantum computing, the Variational Quantum Eigensolver (VQE) stands out as a promising algorithm for solving complex quantum problems, especially in the noisy intermediate-scale quantum (NISQ) era. However, the ubiquitous presence of noise in quantum devices often limits the accuracy and reliability of VQE outcomes. This research introduces a novel approach to ameliorate this challenge by utilizing neural networks for zero noise extrapolation (ZNE) in VQE computations. By employing the Qiskit framework, we crafted parameterized quantum circuits using the RY-RZ ansatz and examined their behavior under varying levels of depolarizing noise. Our investigations spanned from determining the expectation values of a Hamiltonian, defined as a tensor product of Z operators, under different noise intensities to extracting the ground state energy. To bridge the observed outcomes under noise with the ideal noise-free scenario, we trained a Feed Forward Neural Network on the error probabilities and their associated expectation values. Remarkably, our model proficiently predicted the VQE outcome under hypothetical noise-free conditions. By juxtaposing the simulation results with real quantum device executions, we unveiled the discrepancies induced by noise and showcased the efficacy of our neural network-based ZNE technique in rectifying them. This integrative approach not only paves the way for enhanced accuracy in VQE computations on NISQ devices but also underlines the immense potential of hybrid quantum-classical paradigms in circumventing the challenges posed by quantum noise. Through this research, we envision a future where quantum algorithms can be reliably executed on noisy devices, bringing us one step closer to realizing the full potential of quantum computing.

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum-classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.

We investigate the potential of bio-inspired evolutionary algorithms for designing quantum circuits with specific goals, focusing on two particular tasks. The first one is motivated by the ideas of Artificial Life that are used to reproduce stochastic cellular automata with given rules. We test the robustness of quantum implementations of the cellular automata for different numbers of quantum gates The second task deals with the sampling of quantum circuits that generate highly entangled quantum states, which constitute an important resource for quantum computing. In particular, an evolutionary algorithm is employed to optimize circuits with respect to a fitness function defined with the Mayer-Wallach entanglement measure. We demonstrate that, by balancing the mutation rate between exploration and exploitation, we can find entangling quantum circuits for up to five qubits. We also discuss the trade-off between the number of gates in quantum circuits and the computational costs of finding the gate arrangements leading to a strongly entangled state. Our findings provide additional insight into the trade-off between the complexity of a circuit and its performance, which is an important factor in the design of quantum circuits.

Complementary metal-oxide semiconductor (CMOS) technology has radically reshaped the world by taking humanity to the digital age. Cramming more transistors into the same physical space has enabled an exponential increase in computational performance, a strategy that has been recently hampered by the increasing complexity and cost of miniaturization. To continue achieving significant gains in computing performance, new computing paradigms, such as quantum computing, must be developed. However, finding the optimal physical system to process quantum information, and scale it up to the large number of qubits necessary to build a general-purpose quantum computer, remains a significant challenge. Recent breakthroughs in nanodevice engineering have shown that qubits can now be manufactured in a similar fashion to silicon field-effect transistors, opening an opportunity to leverage the know-how of the CMOS industry to address the scaling challenge. In this article, we focus on the analysis of the scaling prospects of quantum computing systems based on CMOS technology.

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that extract information about errors to enable error correction: as higher measurement weights require higher implementation costs and introduce more errors, it is important in code design to optimize measurement weight. This underlies the surging interest in quantum low-density parity-check (qLDPC) codes, the study of which has primarily focused on the asymptotic (large-code-limit) properties. In this work, we introduce a versatile and computationally efficient approach to stabilizer code weight reduction based on reinforcement learning (RL), which produces new low-weight codes that substantially outperform the state of the art in practically relevant parameter regimes, extending significantly beyond previously accessible small distances. For example, our approach demonstrates savings in physical qubit overhead compared to existing results by 1 to 2 orders of magnitude for weight 6 codes and brings the overhead into a feasible range for near-future experiments. We also investigate the interplay between code parameters using our RL framework, offering new insights into the potential efficiency and power of practically viable coding strategies. Overall, our results demonstrate how RL can effectively advance the crucial yet challenging problem of quantum code discovery and thereby facilitate a faster path to the practical implementation of fault-tolerant quantum technologies.

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories and 130,831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench.

In this paper, we propose a novel Hadamard Transform (HT)-based neural network layer for hybrid quantum-classical computing. It implements the regular convolutional layers in the Hadamard transform domain. The idea is based on the HT convolution theorem which states that the dyadic convolution between two vectors is equivalent to the element-wise multiplication of their HT representation. Computing the HT is simply the application of a Hadamard gate to each qubit individually, so the HT computations of our proposed layer can be implemented on a quantum computer. Compared to the regular Conv2D layer, the proposed HT-perceptron layer is computationally more efficient. Compared to a CNN with the same number of trainable parameters and 99.26\% test accuracy, our HT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNIST dataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds the accuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using 11.5\% fewer parameters with 12.6\% fewer MACs.

Classical self-supervised networks suffer from convergence problems and reduced segmentation accuracy due to forceful termination. Qubits or bi-level quantum bits often describe quantum neural network models. In this article, a novel self-supervised shallow learning network model exploiting the sophisticated three-level qutrit-inspired quantum information system referred to as Quantum Fully Self-Supervised Neural Network (QFS-Net) is presented for automated segmentation of brain MR images. The QFS-Net model comprises a trinity of a layered structure of qutrits inter-connected through parametric Hadamard gates using an 8-connected second-order neighborhood-based topology. The non-linear transformation of the qutrit states allows the underlying quantum neural network model to encode the quantum states, thereby enabling a faster self-organized counter-propagation of these states between the layers without supervision. The suggested QFS-Net model is tailored and extensively validated on Cancer Imaging Archive (TCIA) data set collected from Nature repository and also compared with state of the art supervised (U-Net and URes-Net architectures) and the self-supervised QIS-Net model. Results shed promising segmented outcome in detecting tumors in terms of dice similarity and accuracy with minimum human intervention and computational resources.

We present QuantumLLMInstruct (QLMMI), an innovative dataset featuring over 500,000 meticulously curated instruction-following problem-solution pairs designed specifically for quantum computing - the largest and most comprehensive dataset of its kind. Originating from over 90 primary seed domains and encompassing hundreds of subdomains autonomously generated by LLMs, QLMMI marks a transformative step in the diversity and richness of quantum computing datasets. Designed for instruction fine-tuning, QLMMI seeks to significantly improve LLM performance in addressing complex quantum computing challenges across a wide range of quantum physics topics. While Large Language Models (LLMs) have propelled advancements in computational science with datasets like Omni-MATH and OpenMathInstruct, these primarily target Olympiad-level mathematics, leaving quantum computing largely unexplored. The creation of QLMMI follows a rigorous four-stage methodology. Initially, foundational problems are developed using predefined templates, focusing on critical areas such as synthetic Hamiltonians, QASM code generation, Jordan-Wigner transformations, and Trotter-Suzuki quantum circuit decompositions. Next, detailed and domain-specific solutions are crafted to ensure accuracy and relevance. In the third stage, the dataset is enriched through advanced reasoning techniques, including Chain-of-Thought (CoT) and Task-Oriented Reasoning and Action (ToRA), which enhance problem-solution diversity while adhering to strict mathematical standards. Lastly, a zero-shot Judge LLM performs self-assessments to validate the dataset's quality and reliability, minimizing human oversight requirements.

The emerging field of quantum computing has shown it might change how we process information by using the unique principles of quantum mechanics. As researchers continue to push the boundaries of quantum technologies to unprecedented levels, distributed quantum computing raises as an obvious path to explore with the aim of boosting the computational power of current quantum systems. This paper presents a comprehensive survey of the current state of the art in the distributed quantum computing field, exploring its foundational principles, landscape of achievements, challenges, and promising directions for further research. From quantum communication protocols to entanglement-based distributed algorithms, each aspect contributes to the mosaic of distributed quantum computing, making it an attractive approach to address the limitations of classical computing. Our objective is to provide an exhaustive overview for experienced researchers and field newcomers.

The key challenge in the noisy intermediate-scale quantum era is finding useful circuits compatible with current device limitations. Variational quantum algorithms (VQAs) offer a potential solution by fixing the circuit architecture and optimizing individual gate parameters in an external loop. However, parameter optimization can become intractable, and the overall performance of the algorithm depends heavily on the initially chosen circuit architecture. Several quantum architecture search (QAS) algorithms have been developed to design useful circuit architectures automatically. In the case of parameter optimization alone, noise effects have been observed to dramatically influence the performance of the optimizer and final outcomes, which is a key line of study. However, the effects of noise on the architecture search, which could be just as critical, are poorly understood. This work addresses this gap by introducing a curriculum-based reinforcement learning QAS (CRLQAS) algorithm designed to tackle challenges in realistic VQA deployment. The algorithm incorporates (i) a 3D architecture encoding and restrictions on environment dynamics to explore the search space of possible circuits efficiently, (ii) an episode halting scheme to steer the agent to find shorter circuits, and (iii) a novel variant of simultaneous perturbation stochastic approximation as an optimizer for faster convergence. To facilitate studies, we developed an optimized simulator for our algorithm, significantly improving computational efficiency in simulating noisy quantum circuits by employing the Pauli-transfer matrix formalism in the Pauli-Liouville basis. Numerical experiments focusing on quantum chemistry tasks demonstrate that CRLQAS outperforms existing QAS algorithms across several metrics in both noiseless and noisy environments.

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on a quantum device. To guide the selection of measurement methods designed for this observable estimation problem, we propose a benchmark called CSHOREBench (Common States and Hamiltonians for ObseRvable Estimation Benchmark) that assesses the performance of these methods against a set of common molecular Hamiltonians and common states encountered during the runtime of hybrid quantum-classical algorithms. In CSHOREBench, we account for resource utilization of a quantum computer through measurements of a prepared state, and a classical computer through computational runtime spent in proposing measurements and classical post-processing of acquired measurement outcomes. We apply CSHOREBench considering a variety of measurement methods on Hamiltonians of size up to 16 qubits. Our discussion is aided by using the framework of decision diagrams which provides an efficient data structure for various randomized methods and illustrate how to derandomize distributions on decision diagrams. In numerical simulations, we find that the methods of decision diagrams and derandomization are the most preferable. In experiments on IBM quantum devices against small molecules, we observe that decision diagrams reduces the number of measurements made by classical shadows by more than 80%, that made by locally biased classical shadows by around 57%, and consistently require fewer quantum measurements along with lower classical computational runtime than derandomization. Furthermore, CSHOREBench is empirically efficient to run when considering states of random quantum ansatz with fixed depth.

Quantum digital signatures (QDS), generating correlated bit strings among three remote parties for signatures through quantum law, can guarantee non-repudiation, authenticity, and integrity of messages. Recently, one-time universal hashing QDS framework, exploiting the quantum asymmetric encryption and universal hash functions, has been proposed to significantly improve the signature rate and ensure unconditional security by directly signing the hash value of long messages. However, similar to quantum key distribution, this framework utilizes keys with perfect secrecy by performing privacy amplification that introduces cumbersome matrix operations, thereby consuming large computational resources, causing delays and increasing failure probability. Here, we prove that, different from private communication, imperfect quantum keys with limited information leakage can be used for digital signatures and authentication without compromising the security while having eight orders of magnitude improvement on signature rate for signing a megabit message compared with conventional single-bit schemes. This study significantly reduces the delay for data postprocessing and is compatible with any quantum key generation protocols. In our simulation, taking two-photon twin-field key generation protocol as an example, QDS can be practically implemented over a fiber distance of 650 km between the signer and receiver. For the first time, this study offers a cryptographic application of quantum keys with imperfect secrecy and paves a way for the practical and agile implementation of digital signatures in a future quantum network.

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It helps preserve image quality and interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This study introduces a quantum convolutional autoencoder (QCAE) method for improved image denoising. This method was developed by substituting the representative latent space of the autoencoder with a quantum circuit. To enhance efficiency, we leveraged the advantages of the quantum approximate optimization algorithm (QAOA)-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.

Strong correlation brings a rich array of emergent phenomena, as well as a daunting challenge to theoretical physics study. In condensed matter physics, the fractional quantum Hall effect is a prominent example of strong correlation, with Landau level mixing being one of the most challenging aspects to address using traditional computational methods. Deep learning real-space neural network wavefunction methods have emerged as promising architectures to describe electron correlations in molecules and materials, but their power has not been fully tested for exotic quantum states. In this work, we employ real-space neural network wavefunction techniques to investigate fractional quantum Hall systems. On both 1/3 and 2/5 filling systems, we achieve energies consistently lower than exact diagonalization results which only consider the lowest Landau level. We also demonstrate that the real-space neural network wavefunction can naturally capture the extent of Landau level mixing up to a very high level, overcoming the limitations of traditional methods. Our work underscores the potential of neural networks for future studies of strongly correlated systems and opens new avenues for exploring the rich physics of the fractional quantum Hall effect.

Artificial neural networks are the heart of machine learning algorithms and artificial intelligence protocols. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt's `perceptron', but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a perceptron, which shows exponential advantage in encoding resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives remarkably good answers against the expected results. We show that this quantum model of a perceptron can be used as an elementary nonlinear classifier of simple patterns, as a first step towards practical training of artificial quantum neural networks to be efficiently implemented on near-term quantum processing hardware.

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory -- the field that studies the resources (such as time, space, and randomness) needed to solve computational problems -- leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.

Quantum algorithms, represented as quantum circuits, can be used as benchmarks for assessing the performance of quantum systems. Existing datasets, widely utilized in the field, suffer from limitations in size and versatility, leading researchers to employ randomly generated circuits. Random circuits are, however, not representative benchmarks as they lack the inherent properties of real quantum algorithms for which the quantum systems are manufactured. This shortage of `useful' quantum benchmarks poses a challenge to advancing the development and comparison of quantum compilers and hardware. This research aims to enhance the existing quantum circuit datasets by generating what we refer to as `realistic-looking' circuits by employing the Transformer machine learning architecture. For this purpose, we introduce KetGPT, a tool that generates synthetic circuits in OpenQASM language, whose structure is based on quantum circuits derived from existing quantum algorithms and follows the typical patterns of human-written algorithm-based code (e.g., order of gates and qubits). Our three-fold verification process, involving manual inspection and Qiskit framework execution, transformer-based classification, and structural analysis, demonstrates the efficacy of KetGPT in producing large amounts of additional circuits that closely align with algorithm-based structures. Beyond benchmarking, we envision KetGPT contributing substantially to AI-driven quantum compilers and systems.

In recent years, groundbreaking advancements in natural language processing have culminated in the emergence of powerful large language models (LLMs), which have showcased remarkable capabilities across a vast array of domains, including the understanding, generation, and translation of natural language, and even tasks that extend beyond language processing. In this report, we delve into the performance of LLMs within the context of scientific discovery, focusing on GPT-4, the state-of-the-art language model. Our investigation spans a diverse range of scientific areas encompassing drug discovery, biology, computational chemistry (density functional theory (DFT) and molecular dynamics (MD)), materials design, and partial differential equations (PDE). Evaluating GPT-4 on scientific tasks is crucial for uncovering its potential across various research domains, validating its domain-specific expertise, accelerating scientific progress, optimizing resource allocation, guiding future model development, and fostering interdisciplinary research. Our exploration methodology primarily consists of expert-driven case assessments, which offer qualitative insights into the model's comprehension of intricate scientific concepts and relationships, and occasionally benchmark testing, which quantitatively evaluates the model's capacity to solve well-defined domain-specific problems. Our preliminary exploration indicates that GPT-4 exhibits promising potential for a variety of scientific applications, demonstrating its aptitude for handling complex problem-solving and knowledge integration tasks. Broadly speaking, we evaluate GPT-4's knowledge base, scientific understanding, scientific numerical calculation abilities, and various scientific prediction capabilities.

In image processing, the amount of data to be processed grows rapidly, in particular when imaging methods yield images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the Flexible Representation of Quantum Images (FRQI). Furthermore, we check experimentally what is the limit in the current noisy intermediate-scale quantum era, i.e. up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates needed, especially of the error-prone controlled-NOT gates, can be reduced. As a consequence, the size of manageable images increases.

This concept paper aims to provide a brief outline of quantum computers, explore existing methods of quantum image classification techniques, so focusing on remote sensing applications, and discuss the bottlenecks of performing these algorithms on currently available open source platforms. Initial results demonstrate feasibility. Next steps include expanding the size of the quantum hidden layer and increasing the variety of output image options.

A central challenge of the clean energy transition is the development of catalysts for low-emissions technologies. Recent advances in Machine Learning for quantum chemistry drastically accelerate the computation of catalytic activity descriptors such as adsorption energies. Here we introduce AdsorbRL, a Deep Reinforcement Learning agent aiming to identify potential catalysts given a multi-objective binding energy target, trained using offline learning on the Open Catalyst 2020 and Materials Project data sets. We experiment with Deep Q-Network agents to traverse the space of all ~160,000 possible unary, binary and ternary compounds of 55 chemical elements, with very sparse rewards based on adsorption energy known for only between 2,000 and 3,000 catalysts per adsorbate. To constrain the actions space, we introduce Random Edge Traversal and train a single-objective DQN agent on the known states subgraph, which we find strengthens target binding energy by an average of 4.1 eV. We extend this approach to multi-objective, goal-conditioned learning, and train a DQN agent to identify materials with the highest (respectively lowest) adsorption energies for multiple simultaneous target adsorbates. We experiment with Objective Sub-Sampling, a novel training scheme aimed at encouraging exploration in the multi-objective setup, and demonstrate simultaneous adsorption energy improvement across all target adsorbates, by an average of 0.8 eV. Overall, our results suggest strong potential for Deep Reinforcement Learning applied to the inverse catalysts design problem.

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant resources. In this work, we propose a new protocol that combines magic state preparation and code switching to realize logical non-Clifford operations with the potential for fault tolerance. Our approach begins with a special logical state in the Z_4 surface code. By applying a sequence of transformations, the system goes through different topological codes, including the non-Abelian D_4 quantum double model. This process ultimately produces a magic state in a condensed Z_2 surface code, which enables the implementation of a logical T gate in the standard Z_2 surface code. In our analysis, we employ a framework where the topological codes are represented by their topological orders and all the transformations are considered as topological manipulations such as gauging symmetries and condensing anyons. This perspective is particularly useful for understanding code switching between topological codes.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

Quantum computing promises to enhance machine learning and artificial intelligence. Different quantum algorithms have been proposed to improve a wide spectrum of machine learning tasks. Yet, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from the vulnerability problem: adding tiny carefully-crafted perturbations to the legitimate original data samples would facilitate incorrect predictions at a notably high confidence level. This will pose serious problems for future quantum machine learning applications in safety and security-critical scenarios. Here, we report the first experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built upon variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 mus, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4% respectively, with both real-life images (e.g., medical magnetic resonance imaging scans) and quantum data. We demonstrate that these well-trained classifiers (with testing accuracy up to 99%) can be practically deceived by small adversarial perturbations, whereas an adversarial training process would significantly enhance their robustness to such perturbations. Our results reveal experimentally a crucial vulnerability aspect of quantum learning systems under adversarial scenarios and demonstrate an effective defense strategy against adversarial attacks, which provide a valuable guide for quantum artificial intelligence applications with both near-term and future quantum devices.

Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations and hype surrounding quantum computing we ask the question which are the promising applications to realize quantum advantage. We argue that small data problems and quantum algorithms with super-quadratic speedups are essential to make quantum computers useful in practice. With these guidelines one can separate promising applications for quantum computing from those where classical solutions should be pursued. While most of the proposed quantum algorithms and applications do not achieve the necessary speedups to be considered practical, we already see a huge potential in material science and chemistry. We expect further applications to be developed based on our guidelines.

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years, a vast number of MLPs has been trained from scratch because learning additional data typically requires to train again on all data to not forget previously acquired knowledge. Additionally, most common structural descriptors of MLPs cannot represent efficiently a large number of different chemical elements. In this work, we tackle these problems by introducing element-embracing atom-centered symmetry functions (eeACSFs) which combine structural properties and element information from the periodic table. These eeACSFs are a key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pre-trained MLP to arrive at a continuously adapting lMLP, because a predefined level of accuracy can be ensured. To extend the applicability of an lMLP to new systems, we apply continual learning strategies to enable autonomous and on-the-fly training on a continuous stream of new data. For the training of deep neural networks, we propose the continual resilient (CoRe) optimizer and incremental learning strategies relying on rehearsal of data, regularization of parameters, and the architecture of the model.

In this research, we explore the integration of quantum computing with classical machine learning for image classification tasks, specifically focusing on the MNIST dataset. We propose a hybrid quantum-classical approach that leverages the strengths of both paradigms. The process begins with preprocessing the MNIST dataset, normalizing the pixel values, and reshaping the images into vectors. An autoencoder compresses these 784-dimensional vectors into a 64-dimensional latent space, effectively reducing the data's dimensionality while preserving essential features. These compressed features are then processed using a quantum circuit implemented on a 5-qubit system. The quantum circuit applies rotation gates based on the feature values, followed by Hadamard and CNOT gates to entangle the qubits, and measurements are taken to generate quantum outcomes. These outcomes serve as input for a classical neural network designed to classify the MNIST digits. The classical neural network comprises multiple dense layers with batch normalization and dropout to enhance generalization and performance. We evaluate the performance of this hybrid model and compare it with a purely classical approach. The experimental results indicate that while the hybrid model demonstrates the feasibility of integrating quantum computing with classical techniques, the accuracy of the final model, trained on quantum outcomes, is currently lower than the classical model trained on compressed features. This research highlights the potential of quantum computing in machine learning, though further optimization and advanced quantum algorithms are necessary to achieve superior performance.

We propose a quantum version of a generative diffusion model. In this algorithm, artificial neural networks are replaced with parameterized quantum circuits, in order to directly generate quantum states. We present both a full quantum and a latent quantum version of the algorithm; we also present a conditioned version of these models. The models' performances have been evaluated using quantitative metrics complemented by qualitative assessments. An implementation of a simplified version of the algorithm has been executed on real NISQ quantum hardware.

Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing of 3D molecular geometries requires quantum calculations that are computationally prohibitive. For example, accurate calculation of 3D geometries of a small molecule requires hours of computing time using density functional theory (DFT). Here, we propose to predict the ground-state 3D geometries from molecular graphs using machine learning methods. To make this feasible, we develop a benchmark, known as Molecule3D, that includes a dataset with precise ground-state geometries of approximately 4 million molecules derived from DFT. We also provide a set of software tools for data processing, splitting, training, and evaluation, etc. Specifically, we propose to assess the error and validity of predicted geometries using four metrics. We implement two baseline methods that either predict the pairwise distance between atoms or atom coordinates in 3D space. Experimental results show that, compared with generating 3D geometries with RDKit, our method can achieve comparable prediction accuracy but with much smaller computational costs. Our Molecule3D is available as a module of the MoleculeX software library (https://github.com/divelab/MoleculeX).

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use. These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored. We studied the viability of using Projective Simulation, a reinforcement learning technique, to tackle the problem of quantum circuit synthesis for noise quantum computers with limited number of qubits. The agent had the task of creating quantum circuits up to 5 qubits to generate GHZ states in the IBM Tenerife (IBM QX4) quantum processor. Our simulations demonstrated that the agent had a good performance but its capacity for learning new circuits decreased as the number of qubits increased.

In this paper, we delve into the foundational principles of tensor categories, harnessing the universal property of the tensor product to pioneer novel methodologies in deep network architectures. Our primary contribution is the introduction of the Tensor Attention and Tensor Interaction Mechanism, a groundbreaking approach that leverages the tensor category to enhance the computational efficiency and the expressiveness of deep networks, and can even be generalized into the quantum realm.

Quantum computing holds great potential for advancing the limitations of machine learning algorithms to handle higher dimensions of data and reduce overall training parameters in deep learning (DL) models. This study uses a trainable variational quantum circuit (VQC) on a gate-based quantum computing model to investigate the potential for quantum benefit in a model-free reinforcement learning problem. Through a comprehensive investigation and evaluation of the current model and capabilities of quantum computers, we designed and trained a novel hybrid quantum neural network based on the latest Qiskit and PyTorch framework. We compared its performance with a full-classical CNN with and without an incorporated VQC. Our research provides insights into the potential of deep quantum learning to solve a maze problem and, potentially, other reinforcement learning problems. We conclude that reinforcement learning problems can be practical with reasonable training epochs. Moreover, a comparative study of full-classical and hybrid quantum neural networks is discussed to understand these two approaches' performance, advantages, and disadvantages to deep-Q learning problems, especially on larger-scale maze problems larger than 4x4.

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the ``quantisation" of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning [1]. Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models [2]. In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit [3] with the quantum Hamiltonian data embedding unitary [4]. Through numerical experiments on images datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN)[5] by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks.

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.

Quantum programs are typically developed using quantum Software Development Kits (SDKs). The rapid advancement of quantum computing necessitates new tools to streamline this development process, and one such tool could be Generative Artificial intelligence (GenAI). In this study, we introduce and use the Qiskit HumanEval dataset, a hand-curated collection of tasks designed to benchmark the ability of Large Language Models (LLMs) to produce quantum code using Qiskit - a quantum SDK. This dataset consists of more than 100 quantum computing tasks, each accompanied by a prompt, a canonical solution, a comprehensive test case, and a difficulty scale to evaluate the correctness of the generated solutions. We systematically assess the performance of a set of LLMs against the Qiskit HumanEval dataset's tasks and focus on the models ability in producing executable quantum code. Our findings not only demonstrate the feasibility of using LLMs for generating quantum code but also establish a new benchmark for ongoing advancements in the field and encourage further exploration and development of GenAI-driven tools for quantum code generation.

Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits over multiple agents, minimising quantum communication between them. We reduce the problem to hypergraph partitioning and then solve it with state-of-the-art optimisers. This makes our approach useful in practice, unlike previous methods. Our implementation is evaluated on five quantum circuits of practical relevance.

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW'19 paper on QSVT [Gily\'en, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.

Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds.

Binary classical information is routinely encoded in the two metastable states of a dynamical system. Since these states may exhibit macroscopic lifetimes, the encoded information inherits a strong protection against bit-flips. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring bit-flip protection. An outstanding challenge is to gain quantum control over such a system without breaking its protection. If this challenge is met, significant shortcuts in hardware overhead are forecast for quantum computing. In this experiment, we implement a cat-qubit with bit-flip times exceeding ten seconds. This is a four order of magnitude improvement over previous cat-qubit implementations, and six orders of magnitude enhancement over the single photon lifetime that compose this dynamical qubit. This was achieved by introducing a quantum tomography protocol that does not break bit-flip protection. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these superpositions while maintaining the bit-flip time above ten seconds. This work demonstrates quantum operations that preserve macroscopic bit-flip times, a necessary step to scale these dynamical qubits into fully protected hardware-efficient architectures.

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

Recent advances in quantum information science enabled the development of quantum communication network prototypes and created an opportunity to study full-stack quantum network architectures. This work develops SeQUeNCe, a comprehensive, customizable quantum network simulator. Our simulator consists of five modules: Hardware models, Entanglement Management protocols, Resource Management, Network Management, and Application. This framework is suitable for simulation of quantum network prototypes that capture the breadth of current and future hardware technologies and protocols. We implement a comprehensive suite of network protocols and demonstrate the use of SeQUeNCe by simulating a photonic quantum network with nine routers equipped with quantum memories. The simulation capabilities are illustrated in three use cases. We show the dependence of quantum network throughput on several key hardware parameters and study the impact of classical control message latency. We also investigate quantum memory usage efficiency in routers and demonstrate that redistributing memory according to anticipated load increases network capacity by 69.1% and throughput by 6.8%. We design SeQUeNCe to enable comparisons of alternative quantum network technologies, experiment planning, and validation and to aid with new protocol design. We are releasing SeQUeNCe as an open source tool and aim to generate community interest in extending it.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We present strong evidence that commonly used models with provable absence of barren plateaus are also classically simulable, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing quantum computers can be essential for collecting data, our analysis sheds serious doubt on the non-classicality of the information processing capabilities of parametrized quantum circuits for barren plateau-free landscapes. We end by discussing caveats in our arguments, the role of smart initializations and the possibility of provably superpolynomial, or simply practical, advantages from running parametrized quantum circuits.

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time T, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.

Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to generate expressive, nonlinear signals that are efficiently learned with a single linear output layer. We address the need for quantum reservoir tuning with a novel and generally applicable approach to quantum circuit parameterization, in which tunable noise models are programmed to the quantum reservoir circuit to be fully controlled for effective optimization. Our systematic approach also involves reductions in quantum reservoir circuits in the number of qubits and entanglement scheme complexity. We show that with only a single noise model and small memory capacities, excellent simulation results were obtained on nonlinear benchmarks that include the Mackey-Glass system for 100 steps ahead in the challenging chaotic regime.

Within this decade, quantum computers are predicted to outperform conventional computers in terms of processing power and have a disruptive effect on a variety of business sectors. It is predicted that the financial sector would be one of the first to benefit from quantum computing both in the short and long terms. In this research work we use Hybrid Quantum Neural networks to present a quantum machine learning approach for Continuous variable prediction.

Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.

Quantum communication can enhance internet technology by enabling novel applications that are provably impossible classically. The successful execution of such applications relies on the generation of quantum entanglement between different users of the network which meets stringent performance requirements. Alongside traditional metrics such as throughput and jitter, one must ensure the generated entanglement is of sufficiently high quality. Meeting such performance requirements demands a careful orchestration of many devices in the network, giving rise to a fundamentally new scheduling problem. Furthermore, technological limitations of near-term quantum devices impose significant constraints on scheduling methods hoping to meet performance requirements. In this work, we propose the first end-to-end design of a centralized quantum network with multiple users that orchestrates the delivery of entanglement which meets quality-of-service (QoS) requirements of applications. We achieve this by using a centrally constructed schedule that manages usage of devices and ensures the coordinated execution of different quantum operations throughout the network. We use periodic task scheduling and resource-constrained project scheduling techniques, including a novel heuristic, to construct the schedules. Our simulations of four small networks using hardware-validated network parameters, and of a real-world fiber topology using futuristic parameters, illustrate trade-offs between traditional and quantum performance metrics.

The second quantum revolution brings with it the promise of a quantum internet. As the first quantum network hardware prototypes near completion new challenges emerge. A functional network is more than just the physical hardware, yet work on scalable quantum network systems is in its infancy. In this paper we present a quantum network protocol designed to enable end-to-end quantum communication in the face of the new fundamental and technical challenges brought by quantum mechanics. We develop a quantum data plane protocol that enables end-to-end quantum communication and can serve as a building block for more complex services. One of the key challenges in near-term quantum technology is decoherence -- the gradual decay of quantum information -- which imposes extremely stringent limits on storage times. Our protocol is designed to be efficient in the face of short quantum memory lifetimes. We demonstrate this using a simulator for quantum networks and show that the protocol is able to deliver its service even in the face of significant losses due to decoherence. Finally, we conclude by showing that the protocol remains functional on the extremely resource limited hardware that is being developed today underlining the timeliness of this work.

Variational quantum circuits (VQCs) built upon noisy intermediate-scale quantum (NISQ) hardware, in conjunction with classical processing, constitute a promising architecture for quantum simulations, classical optimization, and machine learning. However, the required VQC depth to demonstrate a quantum advantage over classical schemes is beyond the reach of available NISQ devices. Supervised learning assisted by an entangled sensor network (SLAEN) is a distinct paradigm that harnesses VQCs trained by classical machine-learning algorithms to tailor multipartite entanglement shared by sensors for solving practically useful data-processing problems. Here, we report the first experimental demonstration of SLAEN and show an entanglement-enabled reduction in the error probability for classification of multidimensional radio-frequency signals. Our work paves a new route for quantum-enhanced data processing and its applications in the NISQ era.

We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows that, given access to error-free, efficient quantum realizations of the agent and environment, quantum methods can yield provable improvements over classical Monte-Carlo based methods in terms of sample complexity. Our approach shows in detail how to combine amplitude estimation and Grover search into a policy evaluation and improvement scheme. We first develop quantum policy evaluation (QPE) which is quadratically more efficient compared to an analogous classical Monte Carlo estimation and is based on a quantum mechanical realization of a finite Markov decision process (MDP). Building on QPE, we derive a quantum policy iteration that repeatedly improves an initial policy using Grover search until the optimum is reached. Finally, we present an implementation of our algorithm for a two-armed bandit MDP which we then simulate.

In recent years, Classical Convolutional Neural Networks (CNNs) have been applied for image recognition successfully. Quantum Convolutional Neural Networks (QCNNs) are proposed as a novel generalization to CNNs by using quantum mechanisms. The quantum mechanisms lead to an efficient training process in QCNNs by reducing the size of input from N to log_2N. This paper implements and compares both CNNs and QCNNs by testing losses and prediction accuracy on three commonly used datasets. The datasets include the MNIST hand-written digits, Fashion MNIST and cat/dog face images. Additionally, data augmentation (DA), a technique commonly used in CNNs to improve the performance of classification by generating similar images based on original inputs, is also implemented in QCNNs. Surprisingly, the results showed that data augmentation didn't improve QCNNs performance. The reasons and logic behind this result are discussed, hoping to expand our understanding of Quantum machine learning theory.

Quantum machine learning implemented by variational quantum circuits (VQCs) is considered a promising concept for the noisy intermediate-scale quantum computing era. Focusing on applications in quantum reinforcement learning, we propose a specific action decoding procedure for a quantum policy gradient approach. We introduce a novel quality measure that enables us to optimize the classical post-processing required for action selection, inspired by local and global quantum measurements. The resulting algorithm demonstrates a significant performance improvement in several benchmark environments. With this technique, we successfully execute a full training routine on a 5-qubit hardware device. Our method introduces only negligible classical overhead and has the potential to improve VQC-based algorithms beyond the field of quantum reinforcement learning.

This paper presents ``Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the {\em inverse} of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.

Question Answering (QA) has proved to be an arduous challenge in the area of natural language processing (NLP) and artificial intelligence (AI). Many attempts have been made to develop complete solutions for QA as well as improving significant sub-modules of the QA systems to improve the overall performance through the course of time. Questions are the most important piece of QA, because knowing the question is equivalent to knowing what counts as an answer (Harrah in Philos Sci, 1961 [1]). In this work, we have attempted to understand questions in a better way by using Quantum Machine Learning (QML). The properties of Quantum Computing (QC) have enabled classically intractable data processing. So, in this paper, we have performed question classification on questions from two classes of SelQA (Selection-based Question Answering) dataset using quantum-based classifier algorithms-quantum support vector machine (QSVM) and variational quantum classifier (VQC) from Qiskit (Quantum Information Science toolKIT) for Python. We perform classification with both classifiers in almost similar environments and study the effects of circuit depths while comparing the results of both classifiers. We also use these classification results with our own rule-based QA system and observe significant performance improvement. Hence, this experiment has helped in improving the quality of QA in general.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. In this review, we provide both a general introduction and a state of the art description of the recent advances in the field, both theoretically and experimentally. We start by reviewing protocols of quantum key distribution based on discrete variable systems. Next we consider aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems. We will then discuss the ultimate limits of point-to-point private communications and how quantum repeaters and networks may overcome these restrictions. Finally, we will discuss some aspects of quantum cryptography beyond standard quantum key distribution, including quantum data locking and quantum digital signatures.

The emergence of quantum reinforcement learning (QRL) is propelled by advancements in quantum computing (QC) and machine learning (ML), particularly through quantum neural networks (QNN) built on variational quantum circuits (VQC). These advancements have proven successful in addressing sequential decision-making tasks. However, constructing effective QRL models demands significant expertise due to challenges in designing quantum circuit architectures, including data encoding and parameterized circuits, which profoundly influence model performance. In this paper, we propose addressing this challenge with differentiable quantum architecture search (DiffQAS), enabling trainable circuit parameters and structure weights using gradient-based optimization. Furthermore, we enhance training efficiency through asynchronous reinforcement learning (RL) methods facilitating parallel training. Through numerical simulations, we demonstrate that our proposed DiffQAS-QRL approach achieves performance comparable to manually-crafted circuit architectures across considered environments, showcasing stability across diverse scenarios. This methodology offers a pathway for designing QRL models without extensive quantum knowledge, ensuring robust performance and fostering broader application of QRL.

The problem of minimizing the maximum of N convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring O(Nepsilon^{-2/3} + epsilon^{-8/3}) queries to a first-order oracle to compute an epsilon-suboptimal point. On the other hand, quantum algorithms for optimization are rapidly advancing with speedups shown on many important optimization problems. In this paper, we conduct a systematic study for quantum algorithms and lower bounds for minimizing the maximum of N convex, Lipschitz functions. On one hand, we develop quantum algorithms with an improved complexity bound of O(Nepsilon^{-5/3} + epsilon^{-8/3}). On the other hand, we prove that quantum algorithms must take Omega(Nepsilon^{-2/3}) queries to a first order quantum oracle, showing that our dependence on N is optimal up to poly-logarithmic factors.

Classical Internet evolved exceptionally during the last five decades, from a network comprising a few static nodes in the early days to a leviathan interconnecting billions of devices. This has been possible by the separation of concern principle, for which the network functionalities are organized as a stack of layers, each providing some communication functionalities through specific network protocols. In this survey, we aim at highlighting the impossibility of adapting the classical Internet protocol stack to the Quantum Internet, due to the marvels of quantum mechanics. Indeed, the design of the Quantum Internet requires a major paradigm shift of the whole protocol stack for harnessing the peculiarities of quantum entanglement and quantum information. In this context, we first overview the relevant literature about Quantum Internet protocol stack. Then, stemming from this, we sheds the light on the open problems and required efforts toward the design of an effective and complete Quantum Internet protocol stack. To the best of authors' knowledge, a survey of this type is the first of its own. What emerges from this analysis is that the Quantum Internet, though still in its infancy, is a disruptive technology whose design requires an inter-disciplinary effort at the border between quantum physics, computer and telecommunications engineering.

This article aims to investigate how circuit-based hybrid Quantum Convolutional Neural Networks (QCNNs) can be successfully employed as image classifiers in the context of remote sensing. The hybrid QCNNs enrich the classical architecture of CNNs by introducing a quantum layer within a standard neural network. The novel QCNN proposed in this work is applied to the Land Use and Land Cover (LULC) classification, chosen as an Earth Observation (EO) use case, and tested on the EuroSAT dataset used as reference benchmark. The results of the multiclass classification prove the effectiveness of the presented approach, by demonstrating that the QCNN performances are higher than the classical counterparts. Moreover, investigation of various quantum circuits shows that the ones exploiting quantum entanglement achieve the best classification scores. This study underlines the potentialities of applying quantum computing to an EO case study and provides the theoretical and experimental background for futures investigations.

In this paper, we have studied the performance and role of local optimizers in quantum variational circuits. We studied the performance of the two most popular optimizers and compared their results with some popular classical machine learning algorithms. The classical algorithms we used in our study are support vector machine (SVM), gradient boosting (GB), and random forest (RF). These were compared with a variational quantum classifier (VQC) using two sets of local optimizers viz AQGD and COBYLA. For experimenting with VQC, IBM Quantum Experience and IBM Qiskit was used while for classical machine learning models, sci-kit learn was used. The results show that machine learning on noisy immediate scale quantum machines can produce comparable results as on classical machines. For our experiments, we have used a popular restaurant sentiment analysis dataset. The extracted features from this dataset and then after applying PCA reduced the feature set into 5 features. Quantum ML models were trained using 100 epochs and 150 epochs on using EfficientSU2 variational circuit. Overall, four Quantum ML models were trained and three Classical ML models were trained. The performance of the trained models was evaluated using standard evaluation measures viz, Accuracy, Precision, Recall, F-Score. In all the cases AQGD optimizer-based model with 100 Epochs performed better than all other models. It produced an accuracy of 77% and an F-Score of 0.785 which were highest across all the trained models.

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been one of the most interesting areas to study, and it is also one of the biggest problems of biochemistry. Each protein folds distinctively, and the difficulty of finding its stable shape rapidly increases with an increase in the number of amino acids in the chain. A moderate protein has about 100 amino acids, and the number of combinations one needs to verify to find the stable structure is enormous. At some point, the number of these combinations will be so vast that classical computers cannot even attempt to solve them. In this paper, we examine how this problem can be solved with the help of quantum computing using two different algorithms, Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), using Qiskit Nature. We compare the results of different quantum hardware and simulators and check how error mitigation affects the performance. Further, we make comparisons with SoTA algorithms and evaluate the reliability of the method.

In this research, a comparative study of four Quantum Machine Learning (QML) models was conducted for fraud detection in finance. We proved that the Quantum Support Vector Classifier model achieved the highest performance, with F1 scores of 0.98 for fraud and non-fraud classes. Other models like the Variational Quantum Classifier, Estimator Quantum Neural Network (QNN), and Sampler QNN demonstrate promising results, propelling the potential of QML classification for financial applications. While they exhibit certain limitations, the insights attained pave the way for future enhancements and optimisation strategies. However, challenges exist, including the need for more efficient Quantum algorithms and larger and more complex datasets. The article provides solutions to overcome current limitations and contributes new insights to the field of Quantum Machine Learning in fraud detection, with important implications for its future development.

The privacy in classical federated learning can be breached through the use of local gradient results along with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide more privacy. Additionally, sending an N dimensional data vector through a quantum channel requires sending log N entangled qubits, which can potentially provide exponential efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model where fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the coming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model as a quantum state is fed into client-side chips directly; therefore, it does not require measurements on the upcoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over the models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values of these parameters.

We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

Quantum algorithms for optimization problems are of general interest. Despite recent progress in classical lower bounds for nonconvex optimization under different settings and quantum lower bounds for convex optimization, quantum lower bounds for nonconvex optimization are still widely open. In this paper, we conduct a systematic study of quantum query lower bounds on finding epsilon-approximate stationary points of nonconvex functions, and we consider the following two important settings: 1) having access to p-th order derivatives; or 2) having access to stochastic gradients. The classical query lower bounds is Omegabig(epsilon^{-1+p{p}}big) regarding the first setting, and Omega(epsilon^{-4}) regarding the second setting (or Omega(epsilon^{-3}) if the stochastic gradient function is mean-squared smooth). In this paper, we extend all these classical lower bounds to the quantum setting. They match the classical algorithmic results respectively, demonstrating that there is no quantum speedup for finding epsilon-stationary points of nonconvex functions with p-th order derivative inputs or stochastic gradient inputs, whether with or without the mean-squared smoothness assumption. Technically, our quantum lower bounds are obtained by showing that the sequential nature of classical hard instances in all these settings also applies to quantum queries, preventing any quantum speedup other than revealing information of the stationary points sequentially.

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.

This paper introduces the Quantum Generative Diffusion Model (QGDM), a fully quantum-mechanical model for generating quantum state ensembles, inspired by Denoising Diffusion Probabilistic Models. QGDM features a diffusion process that introduces timestep-dependent noise into quantum states, paired with a denoising mechanism trained to reverse this contamination. This model efficiently evolves a completely mixed state into a target quantum state post-training. Our comparative analysis with Quantum Generative Adversarial Networks demonstrates QGDM's superiority, with fidelity metrics exceeding 0.99 in numerical simulations involving up to 4 qubits. Additionally, we present a Resource-Efficient version of QGDM (RE-QGDM), which minimizes the need for auxiliary qubits while maintaining impressive generative capabilities for tasks involving up to 8 qubits. These results showcase the proposed models' potential for tackling challenging quantum generation problems.

Quantum machine learning and vision have come to the fore recently, with hardware advances enabling rapid advancement in the capabilities of quantum machines. Recently, quantum image generation has been explored with many potential advantages over non-quantum techniques; however, previous techniques have suffered from poor quality and robustness. To address these problems, we introduce, MosaiQ, a high-quality quantum image generation GAN framework that can be executed on today's Near-term Intermediate Scale Quantum (NISQ) computers.

The original Grover's algorithm suffers from the souffle problem, which means that the success probability of quantum search decreases dramatically if the iteration time is too small or too large from the right time. To overcome the souffle problem, the fixed-point quantum search with an optimal number of queries was proposed [Phys. Rev. Lett. 113, 210501 (2014)], which always finds a marked state with a high probability when a lower bound of the proportion of marked states is given. The fixed-point quantum search relies on a key lemma regarding the explicit formula of recursive quasi-Chebyshev polynomials, but its proof is not given explicitly. In this work, we give a detailed proof of this lemma, thus providing a sound foundation for the correctness of the fixed-point quantum search. This lemma may be of independent interest as well, since it expands the mathematical form of the recursive relation of Chebyshev polynomials of the first kind, and it also constitutes a key component in overcoming the souffle problem of quantum walk-based search algorithms, for example, robust quantum walk search on complete bipartite graphs [Phys. Rev. A 106, 052207 (2022)]. Hopefully, more applications of the lemma will be found in the future.

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

We present an open-source database of superconducting quantum device designs that may be used as the starting point for customized devices. Each design can be generated programmatically using the open-source Qiskit Metal package, and simulated using finite-element electromagnetic solvers. We present a robust workflow for achieving high accuracy on design simulations. Many designs in the database are experimentally validated, showing excellent agreement between simulated and measured parameters. Our database includes a front-end interface that allows users to generate ``best-guess'' designs based on desired circuit parameters. This project lowers the barrier to entry for research groups seeking to make a new class of devices by providing them a well-characterized starting point from which to refine their designs.

We discuss an algorithm which produces the meaning of a sentence given meanings of its words, and its resemblance to quantum teleportation. In fact, this protocol was the main source of inspiration for this algorithm which has many applications in the area of Natural Language Processing.

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are big(mathcal{O}big(frac 1nbig),,, mathcal{O}big(1{min{m,n}}big)big)-DP under some reasonable restrictions, where m and n are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

Bosonic cat qubits stabilized with a driven two-photon dissipation are systems with exponentially biased noise, opening the door to low-overhead, fault-tolerant and universal quantum computing. However, current gate proposals for such qubits induce substantial noise of the unprotected type, whose poor scaling with the relevant experimental parameters limits their practical use. In this work, we provide a new perspective on dissipative cat qubits by reconsidering the reservoir mode used to engineer the tailored two-photon dissipation, and show how it can be leveraged to mitigate gate-induced errors. Doing so, we introduce four new designs of high-fidelity and bias-preserving cat qubit gates, and compare them to the prevalent gate methods. These four designs should give a broad overview of gate engineering for dissipative systems with different and complementary ideas. In particular, we propose both already achievable low-error gate designs and longer-term implementations.

Deep Reinforcement Learning is emerging as a promising approach for the continuous control task of robotic arm movement. However, the challenges of learning robust and versatile control capabilities are still far from being resolved for real-world applications, mainly because of two common issues of this learning paradigm: the exploration strategy and the slow learning speed, sometimes known as "the curse of dimensionality". This work aims at exploring and assessing the advantages of the application of Quantum Computing to one of the state-of-art Reinforcement Learning techniques for continuous control - namely Soft Actor-Critic. Specifically, the performance of a Variational Quantum Soft Actor-Critic on the movement of a virtual robotic arm has been investigated by means of digital simulations of quantum circuits. A quantum advantage over the classical algorithm has been found in terms of a significant decrease in the amount of required parameters for satisfactory model training, paving the way for further promising developments.

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

Counter-intuitively, quantum mechanics enables quantum particles to propagate simultaneously among multiple space-time trajectories. Hence, a quantum information carrier can travel through different communication channels in a quantum superposition of different orders, so that the relative time-order of the communication channels becomes indefinite. This is realized by utilizing a quantum device known as quantum switch. In this paper, we investigate, from a communication-engineering perspective, the use of the quantum switch within the quantum teleportation process, one of the key functionalities of the Quantum Internet. Specifically, a theoretical analysis is conducted to quantify the performance gain that can be achieved by employing a quantum switch for the entanglement distribution process within the quantum teleportation with respect to the case of absence of quantum switch. This analysis reveals that, by utilizing the quantum switch, the quantum teleportation is heralded as a noiseless communication process with a probability that, remarkably and counter-intuitively, increases with the noise levels affecting the communication channels considered in the indefinite-order time combination.

As a direct consequence of the no-cloning theorem, the deterministic amplification as in classical communication is impossible for quantum states. This calls for more advanced techniques in a future global quantum network, e.g. for cloud quantum computing. A unique solution is the teleportation of an entangled state, i.e. entanglement swapping, representing the central resource to relay entanglement between distant nodes. Together with entanglement purification and a quantum memory it constitutes a so-called quantum repeater. Since the aforementioned building blocks have been individually demonstrated in laboratory setups only, the applicability of the required technology in real-world scenarios remained to be proven. Here we present a free-space entanglement-swapping experiment between the Canary Islands of La Palma and Tenerife, verifying the presence of quantum entanglement between two previously independent photons separated by 143 km. We obtained an expectation value for the entanglement-witness operator, more than 6 standard deviations beyond the classical limit. By consecutive generation of the two required photon pairs and space-like separation of the relevant measurement events, we also showed the feasibility of the swapping protocol in a long-distance scenario, where the independence of the nodes is highly demanded. Since our results already allow for efficient implementation of entanglement purification, we anticipate our assay to lay the ground for a fully-fledged quantum repeater over a realistic high-loss and even turbulent quantum channel.

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Generating entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote entanglement generation have been proposed, of which many have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online.

We introduce the framework of model space into quantum imaginary time evolution (QITE) to enable stable estimation of ground and excited states using a quantum computer. Model-space QITE (MSQITE) propagates a model space to the exact one by retaining its orthogonality, and hence is able to describe multiple states simultaneously. The quantum Lanczos (QLanczos) algorithm is extended to MSQITE to accelerate the convergence. The present scheme is found to outperform both the standard QLanczos and the recently proposed folded-spectrum QITE in simulating excited states. Moreover, we demonstrate that spin contamination can be effectively removed by shifting the imaginary time propagator, and thus excited states with a particular spin quantum number are efficiently captured without falling into the different spin states that have lower energies. We also investigate how different levels of the unitary approximation employed in MSQITE can affect the results. The effectiveness of the algorithm over QITE is demonstrated by noise simulations for the H4 model system.

The ability to communicate quantum information over long distances is of central importance in quantum science and engineering. For example, it enables secure quantum key distribution (QKD) relying on fundamental principles that prohibit the "cloning" of unknown quantum states. While QKD is being successfully deployed, its range is currently limited by photon losses and cannot be extended using straightforward measure-and-repeat strategies without compromising its unconditional security. Alternatively, quantum repeaters, which utilize intermediate quantum memory nodes and error correction techniques, can extend the range of quantum channels. However, their implementation remains an outstanding challenge, requiring a combination of efficient and high-fidelity quantum memories, gate operations, and measurements. Here we report the experimental realization of memory-enhanced quantum communication. We use a single solid-state spin memory integrated in a nanophotonic diamond resonator to implement asynchronous Bell-state measurements. This enables a four-fold increase in the secret key rate of measurement device independent (MDI)-QKD over the loss-equivalent direct-transmission method while operating megahertz clock rates. Our results represent a significant step towards practical quantum repeaters and large-scale quantum networks.

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private numbers, even if using an uncharacterised quantum device potentially built by an adversary. Our generation rates are linear in the repetition rate of the quantum device and the classical randomness post-processing has quasi-linear complexity - making it efficient on a standard personal laptop. The statistical analysis is also tailored for real-world quantum devices. Our protocol is then showcased on several different quantum computers. Although not purposely built for the task, we show that quantum computers can run faithful Bell tests by adding minimal assumptions. In this semi-device-independent manner, our protocol generates (near-)perfectly unbiased and private random numbers on today's quantum computers.

Quantum embedding with transformers is a novel and promising architecture for quantum machine learning to deliver exceptional capability on near-term devices or simulators. The research incorporated a vision transformer (ViT) to advance quantum significantly embedding ability and results for a single qubit classifier with around 3 percent in the median F1 score on the BirdCLEF-2021, a challenging high-dimensional dataset. The study showcases and analyzes empirical evidence that our transformer-based architecture is a highly versatile and practical approach to modern quantum machine learning problems.