Reviewerly/exHarmony huggingface dataset:
Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis

In superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved through injections of large GHZ states. These are prepared using ancillary qubits acting as an “entanglement bus,” unlocking global operation primitives such as multi-qubit Pauli rotations and fan out gates. We derive bounds on the circuit size for several well-studied problems, such as CZ circuit, CX circuit, and Clifford circuit synthesis. In particular, in an architecture using one such entanglement bus, we give an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(n^{3})$</tex> -complexity synthesis scheme for arbitrary Clifford operations requiring at most <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2n+1$</tex> layers of entangled-state-injections. In a square-lattice architecture with two entanglement buses, we show that a graph state can be synthesized using at most <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lceil\frac{1}{2}n\rceil+1$</tex> layers of GHZ state injections, and Clifford operations require only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lceil\frac{3}{2}n\rceil+O(\sqrt{n})$</tex> layers of GHZ state injections.
Unbreakable Security in a Quantum Age: A Systematic Literature Review on Post-Quantum Lattice-Based Standards

The rapid advances in the field of quan-tum computing have led to a concern in the cryp-tographic security implemented in already existing systems. This has led to an increasing interest in the search for post quantum alternatives which are capable of withstanding attacks in the future era of quantum computers. Out of the many approaches that have been put forward, the most promising candidates belong to the class of lattice based cryptography due to their efficient parameter sizes and performances. The robustness of these post quantum schemes have been tested by considering the evaluation criteria which have been put forward by NIST to ensure that the security guarantee provided by these proposed systems are absolute. This paper provides an overview of the various lattice based cryptosystems that have been selected as candidates for standardization by NIST and a comparison between them has been provided demonstrating the differences in their performances on various platforms.
Computational Results for a Quantum Computing Application in Real-Life Finance

This article presents the computational results obtained from a real-life implementation of quantum computing application in investment analytics, which algorithm was described by a previously published paper [5]. The new results reported in this article include: 1) speed-up tests based on idealized problems; 2) speed-ups computed on data from a professional platform, accounting for imperfections on very large financial datasets in finance; and 3) speed-ups from using similar data to solve analogous problems such as implied graphs to explain factor cuts. Furthermore, the article addresses the implementation challenges and computational results, in terms of both speed-ups and error rates, along with any other alternative hardware solutions (if available) such as GPUs for certain users who prefer classical computer solutions. That way, users can compare and contrast the state of the art today and in the foreseeable future. Overall, this article provides insights into the potential of quantum computing to revolutionize the field of finance and highlights the progress made in leveraging artificial intelligence technology for solving real-world problems.
Multidimensional Quantum Convolution with Arbitrary Filtering and Unity Stride

Convolution is a fundamental operation in many critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. Existing implementations of the convolution operator, for example, in quantum neural networks, usually approximate the operation by applying filters with a stride equal to the filter window size. Therefore, it becomes challenging to accurately capture the spatial and temporal locality of the input features, particularly for data of higher dimensions than the commonly-investigated 1-D or 2-D data. Moreover, performing quantum convolution with a unity stride on data of higher dimensions typically requires deep quantum circuits that risk exceeding decoherence constraints. In this work, we propose depth-optimized techniques of implementing multidimensional quantum convolution operations with arbitrary filtering and unity stride. We present theoretical analysis of our techniques and provide the corresponding optimized quantum circuits. We also experimentally demonstrate the applicability of our techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.
QNotation: An Interactive Visual Tool to Lower Learning Barriers in Quantum Computing

One of the first challenges that new learners of Quantum Computing face is learning how to use and interpret quantum circuits represented in circuit, Dirac, and matrix notation. It is necessary for learners to understand the different notations used in Quantum Computing in order to ensure that they have a robust comprehension of the field and can make use of a variety of resources. Depending on their technical background, some learners may struggle with certain notations more than others. We present QNotation, a visual tool that helps learners explore the aforementioned notations. Circuit, Dirac, and matrix notation. This allows them to be able to identify the differences and similarities between the different notations. QNotation was built to be used at multiple stages throughout the Quantum Computer learning journey. While one may start using QNotation to help them become familiar with the different notations used in Quantum Computing, the tool can also be used as a visual quantum circuit debugging tool. In addition to QNotation being a tool that can be used by learners, it can also be used by instructors to support the teachings of quantum computing concepts and building blocks, including entanglement and Quantum Fourier Transform.
Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness

Emerging quantum computing technologies, such as Noisy Intermediate-Scale Quantum (NISQ) devices, offer potential advancements in solving mathematical optimization problems. However, limitations in qubit availability, noise, and errors pose challenges for practical implementation. In this study, we examine two decomposition methods for Mixed-Integer Linear Programming (MILP) designed to reduce the original problem size and utilize available NISQ devices more efficiently. We concentrate on breaking down the original problem into smaller subproblems, which are then solved iteratively using a combined quantum-classical hardware approach. We conduct a detailed analysis for the decomposition of MILP with Benders and Dantzig-Wolfe methods. In our analysis, we show that the number of qubits required to solve Benders is exponentially large in the worst-case, while remains constant for Dantzig-Wolfe. Additionally, we leverage Dantzig-Wolfe decomposition on the use-case of certifying the robustness of ReLU networks. Our experimental results demonstrate that this approach can save up to 90% of qubits compared to existing methods on quantum annealing and gate-based quantum computers.
Robustness of Quantum Algorithms Against Approximate Data Representations

Quantum algorithms face practical difficulties and overheads in execution on realistic devices, potentially thwarting their theoretical advantages. A key practical challenge is efficiently encoding classical data, since data embedding layers, often exponential in the number of qubits, can consume a significant portion of the circuit depth. One possible strategy to address this is to compress the standard data embeddings using variational circuits. The approximate amplitude encoding (AAE) algorithm successfully applies this approach to financial calculations and image pattern matching, achieving only polynomially deep embedding layers. While prior works focus on optimizing the approximate embedding in isolation, the ultimate goal is the compound algorithm's performance. This study systematically examines the impact of embedding compression on the fidelity of the subsequent quantum algorithm in a noiseless setting, specifically investigating amplitude encoding and its dependence on input data set size and complexity. Trainability of the different variational ansaetze, their output state fidelity, and the degree of the embedding layer depth compression are investigated. Performance benchmarks of standard quantum algorithms, e.g. Grover search, amplitude estimation, and quantum Fourier transform (QFT), are conducted based on the degree of compression and quality of the compressed input state. Results show that the amplitude encoding circuit can be compressed substantially in depth, for generic data and a small number of qubits, with only marginal loss in state fidelity. Certain algorithms, like QFT, demonstrate robustness to such approximations.
Fight or Flight: Cosmic Ray-Induced Phonons and the Quantum Surface Code<sup>*</sup>

Recent work has identified cosmic ray events as an error source limiting the lifetime of quantum data. These errors are correlated and affect a large number of qubits, leading to the loss of data across a quantum chip. Previous works attempting to address the problem in hardware or by building distributed systems still have limitations. We approach the problem from a different perspective, developing a new hybrid hardware-software-based strategy based on the 2-D surface code, assuming the parallel development of a hardware strategy that limits the phonon propagation radius. We propose to flee the area: move the logical qubits far enough away from the strike's epicenter to maintain our logical information. Specifically, we: (1) establish the minimum hardware requirements needed for our approach; (2) propose a mapping for moving logical qubits; and (3) evaluate the possible choice of the code distance. Our analysis considers two possible cosmic ray events: those far from both “holes” in the surface code and those near or overlapping a hole. We show that the probability that the logical qubit will be destroyed can be reduced from 100% to the range 4% to 15% depending on the time required to move the logical qubit,
Improving Performance in Combinatorial Optimization Problems with Inequality Constraints: An Evaluation of the Unbalanced Penalization Method on D-Wave Advantage

Combinatorial optimization problems are one of the target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to Ising Hamiltonians using the quadratic unconstrained binary optimization (QUBO) formulation. Many of these applications have inequality constraints, usually encoded as penalization terms in the QUBO formulation using additional variables known as slack variables. The slack variables have two disadvantages: (i) these variables extend the search space of optimal and suboptimal solutions, and (ii) the variables add extra qubits and connections to the quantum algorithm. Recently, a new method known as unbalanced penalization has been presented to avoid using slack variables. This method offers a trade-off between additional slack variables to ensure that the optimal solution is given by the ground state of the Ising Hamiltonian, and using an unbalanced heuristic function to penalize the region where the inequality constraint is violated with the only certainty that the optimal solution will be in the vicinity of the ground state. This work tests the unbalanced penalization method using real quantum hardware on D-Wave Advantage for the traveling salesman problem (TSP). The results show that the unbalanced penalization method outperforms the solutions found using slack variables and sets a new record for the largest TSP solved with quantum technology.
Optimality Despite Chaos in Fee Markets

Transaction fee markets are essential components of blockchain economies, as they resolve the inherent scarcity in the number of transactions that can be added to each block. In early blockchain protocols, this scarcity was resolved through a first-price auction in which users were forced to guess appropriate bids from recent blockchain data. Ethereum’s EIP-1559 fee market reform streamlines this process through the use of a base fee that is increased (or decreased) whenever a block exceeds (or fails to meet) a specified target block size. Previous work has found that the EIP-1559 mechanism may lead to a base fee process that is inherently chaotic, in which case the base fee does not converge to a fixed point even under ideal conditions. However, the impact of this chaotic behavior on the fee market’s main design goal – blocks whose long-term average size equals the target – has not previously been explored. As our main contribution, we derive near-optimal upper and lower bounds for the time-average block size in the EIP-1559 mechanism despite its possibly chaotic evolution. Our lower bound is equal to the target utilization level whereas our upper bound is $$\approx \!6\%$$ higher than optimal. Empirical evidence is shown in great agreement with these theoretical predictions. Specifically, the historical average was $$\approx \!2.9\%$$ larger than the target rage under Proof-of-Work and decreased to $$\approx \!2.0\%$$ after Ethereum’s transition to Proof-of-Stake. We also find that an approximate version of EIP-1559 achieves optimality even in the absence of convergence.
Taiwan Student Quantum Computer Society

In Taiwan, we founded a student-created and led community-Student Quantum Computer Society (SQCS) mainly for high school students. SQCS inspires people in quantum technology via the internet and self-learning, providing traditional Chinese learning opportunities. We provide three pathways including (1) Information and News, (2) Quantum Courses, and (3) Platforms to promote quantum technology in Taiwan. In Information and News, SQCS provides popular science reports and news for aspiring learners. In Quantum Courses, SQCS provides three different methods: Quantum workshops, Quantum micro-courses, and online courses. In online platforms, SQCS established a Discord server for aspiring learners and professionals to communicate, cooperate, and bond with each other. Until now, SQCS is the largest quantum online community in Taiwan. SQCS designs courses not only for high school level but also for college students majoring in science and technology. This provides more opportunities for self-learning and acquiring knowledge because of the Internet. We truly hope that more and more countries will establish their own community and stimulate academic exchange between communities, further establishing an international community with quantum lovers and advocates.
The maximum-likelihood quantum amplitude estimation algorithm provides the best tradeoff between accuracy and circuit depth among quantum solutions for integral estimation

The approximation of an integral with numerical integration methods is a relevant problem in many fields, from finance to chemistry. Monte Carlo methods are a family of methods widely used for numerical integration but which are not always applicable to industrial tasks. Instead, there are quantum computing methods such as Quantum Amplitude Estimation able to offer a speed-up compared to the Monte Carlo methods for numerical integration which promise a significant impact, especially in finance. The Quantum Amplitude Estimation algorithm is a fundamental quantum algorithm with the potential to achieve a quadratic speed-up. Unfortunately, being competitive over classical Monte Carlo methods would require hardware performances currently not available. Therefore, alternative methods have been developed in order to exploit fewer resources while maintaining an advantageous theoretical scaling. We present a comparison between the standard QAE algorithm and two NISQ-friendly versions of the QAE on a numerical integration task. The Monte Carlo technique of Metropolis-Hastings instead is used as a classical benchmark. The scaling of the different algorithms are evaluated in terms of estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the quantum solutions. The conclusion highlights that an alternative approach is preferable with respect to employng the phase estimation routine. Indeed, the maximum likelihood estimation guarantees the best trade-off between the length of the quantum circuits and the precision in the integral estimation.
Benchmarking Adaptive Quantum Circuit Optimization Algorithms for Quantum Chemistry

In the noisy near-term quantum computing era variational quantum algorithms are promising to explore the boundaries of quantum advantage. One prevalent instance is the variational quantum eigensolver (VQE) employed in quantum chemistry to approximate ground-state energies of molecules. The performance of VQE depends on the design of the parametrized quantum circuit, as well as the optimization algorithm used to optimize those parameters. Circuit optimization methods have been developed to generate quantum circuits to reach accurate approximations to the ground-states. In this work, we conduct an empirical comparison between two prominent adaptive quantum circuit optimization algorithms, namely qubit-ADAPT-VQE and a reinforcement learning (RL) based method, on the problem of finding the ground state energy of Lithium Hydride (LiH). In our experiment, we focus on the circuit depth generated by each circuit optimization method and the number of two-qubit quantum gates in the best-found circuit.
Hybrid Classical-Quantum Computing: Are we Forgetting the Classical Part in the Binomial?

The expectations arising from the latest achievements in the quantum computing field are causing that researchers coming from classical artificial intelligence to be fascinated by this new paradigm. In turn, quantum computing, on the road towards usability, needs classical procedures. Hybridization is, in these circumstances, an indispensable step but can also be seen as a promising new avenue to get the most from both computational worlds. Nonetheless, hybrid approaches have now and will have in the future many challenges to face, which, if ignored, will threaten the viability or attractiveness of quantum computing for real-world applications. To identify them and pose pertinent questions, a proper characterization of the hybrid quantum computing field, and especially hybrid solvers, is compulsory. With this motivation in mind, the main purpose of this work is to propose a preliminary taxonomy for classifying hybrid schemes, and bring to the fore some questions to stir up researchers minds about the real challenges regarding the application of quantum computing.
A Reconfigurable Quantum State Tomography Solver in FPGA

In this work, we present an efficient, reconfigurable solution to the memory- and compute-expensive problem of quantum state tomography implemented in an FPGA architecture. Based on the unique characteristics of the closed-form least squares solution for tomographically complete quantum measurement sets, we are able to encode the necessary infor-mation for any multi-qubit system into an algorithm-hardware co-design scheme and solve for the quantum state yielding the measurement results without any traditional multiplication or division blocks in FPGA. We demonstrate this method on a basic Pynq-Z2 FPGA with various approaches resulting in exponential speedup over both direct closed-form implementation and opti-mizer methods with negligible accuracy loss. This architecture is easily reconfigurable to any number of qubits and enables rapid reconstruction of quantum states from measurement data in order to improve real-time compute applications such as quantum hardware calibration, with further applications to quantum process tomography and rapidly analyzing complex many-qubit system dynamics.
Solving Graph Problems with Single-Photons and Linear Optics

An important challenge for current and near-term quantum devices is finding useful tasks that can be preformed on them. We first show how to efficiently encode a bounded <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n\times n$</tex> matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A$</tex> into a linear optical circuit with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2n$</tex> modes. We then apply this encoding to the case where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A$</tex> is a matrix containing information about a graph <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$G$</tex> . We show that a photonic quantum processor consisting of single-photon sources, a linear optical circuit encoding <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A$</tex> , and single-photon detectors can solve a range of graph problems including finding the number of perfect matchings of bipartite graphs, computing permanental polynomials, determining whether two graphs are isomorphic, and the k-densest subgraph problem. We also propose pre-processing methods to boost the probabilities of observing the relevant detection events and thus improve performance. Finally we present both numerical simulations and implementations on Quandela's Ascella photonic quantum processor to validate our findings.
Quantum Algorithm for the Linear Vlasov Equation with Collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. This representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.