[ { "text": "Trapping ions with lasers: This work theoretically addresses the trapping an ionized atom with a single\nvalence electron by means of lasers, analyzing qualitatively and quantitatively\nthe consequences of the net charge of the particle. In our model, the coupling\nbetween the ion and the electromagnetic field includes the charge monopole and\nthe internal dipole, within a multipolar expansion of the interaction\nHamiltonian. Specifically, we perform a Power-Zienau-Woolley transformation,\ntaking into account the motion of the center of mass. The net charge produces a\ncorrection in the atomic dipole which is of order $m_e/M$ with $m_e$ the\nelectron mass and $M$ the total mass of the ion. With respect to neutral atoms,\nthere is also an extra coupling to the laser field which can be approximated by\nthat of the monopole located at the position of the center of mass. These\nadditional effects, however, are shown to be very small compared to the\ndominant dipolar trapping term.", "category": "quant-ph" }, { "text": "X-entanglement of PDC photon pairs: We investigate the spatio-temporal structure of the bi-photon entanglement in\nparametric down-conversion (PDC) and we demonstrate its non-factorable X-shaped\ngeometry. Such a structure gives access to the ultra-broad bandwidth of PDC,\nand can be exploited to achieve a bi-photon temporal localization in the\nfemtosecond range. This extreme localization is connected to our ability to\nresolve the photon positions in the source near-field. The non factorability\nopens the possibility of tailoring the temporal entanglement by acting on the\nspatial degrees of freedom of twin photons.", "category": "quant-ph" }, { "text": "Exact Bethe ansatz spectrum of a tight-binding chain with dephasing\n noise: We construct an exact map between a tight-binding model on any bipartite\nlattice in presence of dephasing noise and a Hubbard model with imaginary\ninteraction strength. In one dimension, the exact many-body Liouvillian\nspectrum can be obtained by application of the Bethe ansatz method. We find\nthat both the non-equilibrium steady state and the leading decay modes\ndescribing the relaxation at late times are related to the eta-pairing symmetry\nof the Hubbard model. We show that there is a remarkable relation between the\ntime-evolution of an arbitrary k-point correlation function in the dissipative\nsystem and k-particle states of the corresponding Hubbard model.", "category": "quant-ph" }, { "text": "Resource estimate for quantum many-body ground-state preparation on a\n quantum computer: We estimate the resources required to prepare the ground state of a quantum\nmany-body system on a quantum computer of intermediate size. This estimate is\nmade possible using a combination of quantum many-body methods and analytic\nupper bounds. Our routine can also be used to optimize certain design\nparameters for specific problem instances. Lastly, we propose and benchmark an\nimproved quantum state preparation procedure. We find that it reduces the\ncircuit T-depth by a factor as large as $10^6$ for intermediate-size lattices.", "category": "quant-ph" }, { "text": "Completely positive completely positive maps (and a resource theory for\n non-negativity of quantum amplitudes): In this work we examine quantum states which have non-negative amplitudes (in\na fixed basis) and the channels which preserve them. These states include the\nground states of stoquastic Hamiltonians and they are of interest since they\navoid the Sign Problem and can thus be efficiently simulated. In optimization\ntheory, the convex cone generated by such states is called the set of\ncompletely positive (CP) matrices (not be confused with completely positive\nsuperoperators). We introduce quantum channels which preserve these states and\ncall them completely positive completely positive. To study these states and\nchannels, we use the framework of resource theories and investigate how to\nmeasure and quantify this resource.", "category": "quant-ph" }, { "text": "Computation on a Noiseless Quantum Code and Symmetrization: Let ${\\cal H}$ be the state-space of a quantum computer coupled with the\nenvironment by a set of error operators spanning a Lie algebra ${\\cal L}.$\nSuppose ${\\cal L}$ admits a noiseless quantum code i.e., a subspace ${\\cal\nC}\\subset{\\cal H}$ annihilated by ${\\cal L}.$ We show that a universal set of\ngates over $\\cal C$ is obtained by any generic pair of ${\\cal L}$-invariant\ngates. Such gates - if not available from the outset - can be obtained by\nresorting to a symmetrization with respect to the group generated by ${\\cal\nL}.$ Any computation can then be performed completely within the coding\ndecoherence-free subspace.", "category": "quant-ph" }, { "text": "Stable single-photon interference in a 1 km fiber-optical Mach-Zehnder\n interferometer with continuous phase adjustment: We experimentally demonstrate stable and user-adjustable single-photon\ninterference in a 1 km long fiber- optical Mach-Zehnder interferometer, using\nan active phase control system with the feedback provided by a classical laser.\nWe are able to continuously tune the single-photon phase difference between the\ninterferometer arms using a phase modulator, which is synchronized with the\ngate window of the single-photon detectors. The phase control system employs a\npiezoelectric fiber stretcher to stabilize the phase drift in the\ninterferometer. A single-photon net visibility of 0.97 is obtained, yielding\nfuture possibilities for experimental realizations of quantum repeaters in\noptical fibers, and violation of Bell's inequalities using genuine energy-time\nentanglement", "category": "quant-ph" }, { "text": "Optical Shelving: Suppressed Fluorescence: The shelving phenomenon of quantum optics, originally observed by Dehmelt, is\nanalyzed in terms of the qRules that are given in another paper. The heuristic\nvalue of these rules is apparent because they not only describe the dark period\nduring shelving, but they reveal the mechanism that enforces the suppression of\nfluorescence during that time.", "category": "quant-ph" }, { "text": "Coarsening Measurement References and the Quantum-to-Classical\n Transition: We investigate the role of inefficiency in quantum measurements in the\nquantum-to-classical transition, and consistently observe the\nquantum-to-classical transition by coarsening the references of the\nmeasurements (e.g. when and where to measure). Our result suggests that the\ndefinition of measurement precision in quantum theory should include the degree\nof the observer's ability to precisely control the measurement references.", "category": "quant-ph" }, { "text": "When is a set of questions to nature together with sharp answers to\n those questions in one-to-one correspondence with a set of quantum states?: A general question is posed to the quantum community. Partial results are\nformulated in a self-contained way. In particular, the title question is\nanswered affirmatorily in two cases: 1) The case of spin/ angular momentum of a\npartcle; 2) A general symmetry situation under certain technical assumptions.", "category": "quant-ph" }, { "text": "On the Probabilistic Compatibility of Special Relativity and Quantum\n Mechanics: In this paper we introduce the three main notions of probability used by\nphysicists and discuss how these are to be used when invoking spacelike\nseparated observers in a relativistic format. We discuss a standard EPRB\nexperiment and concentrate upon problems of the interpretation of\nprobabilities. We promote a particularly conservative interpretation of this\nexperiment (which need not invoke an objective notion of collapse) where\nprobabilities are, tentatively, passively Lorentz invariant. We also argue that\nthe Heisenberg picture is preferable in relativistic situations due to a\nconflict between the Schrodinger picture and passive Lorentz transformations of\nprobabilities. Throughout most of this paper we discuss the relative frequency\ninterpretation of probability as this is most commonly used. We also introduce\nthe logically necessary notion of `prior-frequency' in discussing whether the\nchoice by an observer can have any causal effect upon the measurement results\nof another. We also critically examine the foundational use of relative\nfrequency in no-signalling theorems. We argue that SQT and SR are\nprobabilistically compatible, although we do not discuss whether they are\ncompatible on the level of individual events.", "category": "quant-ph" }, { "text": "Origin of the Canonical Ensemble: Thermalization with Decoherence: We solve the time-dependent Schrodinger equation for the combination of a\nspin system interacting with a spin bath environment. In particular, we focus\non the time development of the reduced density matrix of the spin system. Under\nnormal circumstances we show that the environment drives the reduced density\nmatrix to a fully decoherent state, and furthermore the diagonal elements of\nthe reduced density matrix approach those expected for the system in the\ncanonical ensemble. We show one exception to the normal case is if the spin\nsystem cannot exchange energy with the spin bath. Our demonstration does not\nrely on time-averaging of observables nor does it assume that the coupling\nbetween system and bath is weak. Our findings show that the canonical ensemble\nis a state that may result from pure quantum dynamics, suggesting that quantum\nmechanics may be regarded as the foundation of quantum statistical mechanics.", "category": "quant-ph" }, { "text": "Fast quantum logic gates with trapped-ion qubits: Quantum bits based on individual trapped atomic ions constitute a promising\ntechnology for building a quantum computer, with all the elementary operations\nhaving been achieved with the necessary precision for some error-correction\nschemes. However, the essential two-qubit logic gate used for generating\nquantum entanglement has hitherto always been performed in an adiabatic regime,\nwhere the gate is slow compared with the characteristic motional frequencies of\nions in the trap, giving logic speeds of order 10kHz. There have been numerous\nproposals for performing gates faster than this natural \"speed limit\" of the\ntrap. We implement the method of Steane et al., which uses tailored laser\npulses: these are shaped on 10 ns timescales to drive the ions' motion along\ntrajectories designed such that the gate operation is insensitive to optical\nphase fluctuations. This permits fast (MHz-rate) quantum logic which is robust\nto this important source of experimental error. We demonstrate entanglement\ngeneration for gate times as short as 480ns; this is less than a single\noscillation period of an ion in the trap, and 8 orders of magnitude shorter\nthan the memory coherence time measured in similar calcium-43 hyperfine qubits.\nThe method's power is most evident at intermediate timescales, where it yields\na gate error more than ten times lower than conventional techniques; for\nexample, we achieve a 1.6 us gate with fidelity 99.8%. Still faster gates are\npossible at the price of higher laser intensity. The method requires only a\nsingle amplitude-shaped pulse and one pair of beams derived from a\ncontinuous-wave laser, and offers the prospect of combining the unrivalled\ncoherence properties, operation fidelities and optical connectivity of\ntrapped-ion qubits with the sub-microsecond logic speeds usually associated\nwith solid state devices.", "category": "quant-ph" }, { "text": "Quantum Zeno and Anti-Zeno Effects on the Entanglement Dynamics of\n Qubits Dissipating into a Common and non-Markovian Environment: We investigate the quantum Zeno and anti-Zeno effects on pairwise\nentanglement dynamics of a collective of non-interacting qubits which have been\ninitially prepared in a Werner state and are off-resonantly coupled to a common\nand non-Markovian environment. We obtain the analytical expression of the\nconcurrence in the absence and presence of the non-selective measurements. In\nparticular, we express our results in the strong and weak coupling regimes and\nexamine the role of the system size, and the effect of the detuning from the\ncavity field frequency on the temporal behaviour of the pairwise entanglement.\nWe show that, the detuning parameter has a positive role in the protection of\nentanglement in the absence of the measurement for weak coupling regime. We\nfind that for the values of detuning parameter less than the cavity damping\nrate, the quantum Zeno effect is always dominant, while for the values greater\nthan the cavity damping rate, both Zeno and anti-Zeno effects can occur,\ndepending on the measurement intervals. We also find that the anti-Zeno effect\ncan occur in the pairwise entanglement dynamics in the absence and presence of\nthe detuning in the strong coupling regime.", "category": "quant-ph" }, { "text": "Computation at a distance: We consider a model of computation motivated by possible limitations on\nquantum computers. We have a linear array of n wires, and we may perform\noperations only on pairs of adjacent wires. Our goal is to build a circuits\nthat perform specified operations spanning all n wires. We show that the\nnatural lower bound of n-1 on circuit depth is nearly tight for a variety of\nproblems, and we prove linear upper bounds for additional problems. In\nparticular, using only gates adding a wire (mod 2) into an adjacent wire, we\ncan realize any linear operation in GL_n(2) as a circuit of depth 5n. We show\nthat some linear operations require depth at least 2n+1.", "category": "quant-ph" }, { "text": "Casimir Friction Force and Energy Dissipation for Moving Harmonic\n Oscillators: The Casimir friction problem for a pair of dielectric particles in relative\nmotion is analyzed, utilizing a microscopic model in which we start from\nstatistical mechanics for harmonically oscillating particles at finite\ntemperature moving nonrelativistically with constant velocity. The use of\nstatistical mechanics in this context has in our opinion some definite\nadvantages, in comparison with the more conventional quantum electrodynamic\ndescription of media that involves the use of a refractive index. The\nstatistical-mechanical description is physical and direct, and the oscillator\nmodel, in spite of its simplicity, is nevertheless able to elucidate the\nessentials of the Casimir friction. As is known, there are diverging opinions\nabout this kind of friction in the literature. Our treatment elaborates upon,\nand extends, an earlier theory presented by us back in 1992. There we found a\nfinite friction force at any finite temperature, whereas at zero temperature\nthe model led to a zero force. As an additional development in the present\npaper we evaluate the energy dissipation making use of an exponential cutoff\ntruncating the relative motion of the oscillators. For the dissipation we also\nestablish a general expression that is not limited to the simple oscillator\nmodel.", "category": "quant-ph" }, { "text": "Decoherence in closed and open systems: A generalized formal framework for decoherence, that can be used both in open\nand closed quantum systems, is sketched. In this context, the relationship\nbetween the decoherence of a closed system and the decoherence of its\nsubsystems is studied, and the corresponding decoherence times are defined: for\nmacroscopic systems, the decoherence time of the closed system is much greater\nthan the decoherence time of its subsystems. Finally, it is shown that the\napplication of the new formal framework to a well-known model leads to\nphysically adequate results.", "category": "quant-ph" }, { "text": "Mana in Haar-random states: Mana is a measure of the amount of non-Clifford resources required to create\na state; the mana of a mixed state on $\\ell$ qudits bounded by $\\le \\frac 1 2\n(\\ell \\ln d - S_2)$; $S_2$ the state's second Renyi entropy. We compute the\nmana of Haar-random pure and mixed states and find that the mana is nearly\nlogarithmic in Hilbert space dimension: that is, extensive in number of qudits\nand logarithmic in qudit dimension. In particular, the average mana of states\nwith less-than-maximal entropy falls short of that maximum by $\\ln \\pi/2$. We\nthen connect this result to recent work on near-Clifford approximate\n$t$-designs; in doing so we point out that mana is a useful measure of\nnon-Clifford resources precisely because it is not differentiable.", "category": "quant-ph" }, { "text": "Improved protocols of secure quantum communication using W states: Recently, Hwang et al. [Eur. Phys. J. D. 61, 785 (2011)] and Yuan et al.\n[Int. J. Theo. Phys. 50, 2403 (2011)] have proposed two efficient protocols of\nsecure quantum communication using 3-qubit and 4-qubit symmetric W state\nrespectively. These two dense coding based protocols are generalized and their\nefficiencies are considerably improved. Simple bounds on the qubit efficiency\nof deterministic secure quantum communication (DSQC) and quantum secure direct\ncommunication (QSDC) protocols are obtained and it is shown that dense coding\nis not essential for designing of maximally efficient DSQC and QSDC protocols.\nThis fact is used to design maximally efficient protocols of DSQC and QSDC\nusing 3-qubit and 4-qubit W states.", "category": "quant-ph" }, { "text": "The magnetic field generated by an electron bound in angular-momentum\n eigenstates: The magnetic field generated by an electron bound in a spherically symmetric\npotential is calculated for eigenstates of the orbital and total angular\nmomentum. General expressions are presented for the current density in such\nstates and the magnetic field is calculated through the vector potential, which\nis obtained from the current density by direct integration. The method is\napplied to the hydrogen atom, for which we reproduce and extend known results.", "category": "quant-ph" }, { "text": "Small Majorana Fermion Codes: We consider Majorana fermion stabilizer codes with small number of modes and\ndistance. We give an upper bound on the number of logical qubits for distance\n$4$ codes, and we construct Majorana fermion codes similar to the classical\nHamming code that saturate this bound. We perform numerical studies and find\nother distance $4$ and $6$ codes that we conjecture have the largest possible\nnumber of logical qubits for the given number of physical Majorana modes. Some\nof these codes have more logical qubits than any Majorana fermion code derived\nfrom a qubit stabilizer code.", "category": "quant-ph" }, { "text": "Many-body localization in waveguide QED: At the quantum many-body level, atom-light interfaces generally remain\nchallenging to solve for or understand in a non-perturbative fashion. Here, we\nconsider a waveguide quantum electrodynamics model, where two-level atoms\ninteract with and via propagating photons in a one-dimensional waveguide, and\nspecifically investigate the interplay of atomic position disorder, multiple\nscattering of light, quantum nonlinear interactions and dissipation. We develop\nqualitative arguments and present numerical evidence that such a system\nexhibits a many-body localized~(MBL) phase, provided that atoms are less than\nhalf excited. Interestingly, while MBL is usually formulated with respect to\nclosed systems, this system is intrinsically open. However, as dissipation\noriginates from transport of energy to the system boundaries and the subsequent\nradiative loss, the lack of transport in the MBL phase makes the waveguide QED\nsystem look essentially closed and makes applicable the notions of MBL.\nConversely, we show that if the system is initially in a delocalized phase due\nto a large excitation density, rapid initial dissipation can leave the system\nunable to efficiently transport energy at later times, resulting in a dynamical\ntransition to an MBL phase. These phenomena can be feasibly realized in\nstate-of-the-art experimental setups.", "category": "quant-ph" }, { "text": "Exactly Solvable Sextic Potential Having Symmetric Triple-Well Structure: In this paper, we introduce a family of sextic potentials that are exactly\nsolvable, and for the first time, a family of triple-well potentials with their\nwhole energy spectrum and wavefunctions using supersymmetry method. It was\nsuggested since three decades ago that all \"additive\" or \"translational\" shape\ninvariant superpotentials formed by two combination of functions have been\nfound and their list was already exhausted by the well-known exactly solvable\npotentials that are available in most textbooks and furthermore, there are no\nothers. We have devised a new family of superpotentials formed by a linear\ncombination of three functions (two monomials and one rational) and where the\nchange of parameter function is linear in four parameters. This new family of\npotentials with superpotential $W(x,A,B,D,G) = Ax^3 + Bx -\\frac{Dx}{1+Gx^2}$\nwill extend the list of exactly solvable Schr\\\"odinger equations. We have shown\nthat the energy of the bound states is rational in the quantum number.\nFurthermore, approximating the potential around the central well by a harmonic\noscillator, as a usual practice, is not valid. The two outer wells affect\nnoticeably the probability density distribution of the excited states. We have\nnoticed that the populations of the triple-well potentials are localized in the\ntwo outer wells. These results have potential applications to explore more\nphysical phenomena such as tunneling effect, and instantons dynamics.", "category": "quant-ph" }, { "text": "sQUlearn $\\unicode{x2013}$ A Python Library for Quantum Machine Learning: sQUlearn introduces a user-friendly, NISQ-ready Python library for quantum\nmachine learning (QML), designed for seamless integration with classical\nmachine learning tools like scikit-learn. The library's dual-layer architecture\nserves both QML researchers and practitioners, enabling efficient prototyping,\nexperimentation, and pipelining. sQUlearn provides a comprehensive toolset that\nincludes both quantum kernel methods and quantum neural networks, along with\nfeatures like customizable data encoding strategies, automated execution\nhandling, and specialized kernel regularization techniques. By focusing on\nNISQ-compatibility and end-to-end automation, sQUlearn aims to bridge the gap\nbetween current quantum computing capabilities and practical machine learning\napplications.", "category": "quant-ph" }, { "text": "Symmetric blind information reconciliation and hash-function-based\n verification for quantum key distribution: We consider an information reconciliation protocol for quantum key\ndistribution (QKD). In order to correct down the error rate, we suggest a\nmethod, which is based on symmetric blind information reconciliation for the\nlow-density parity-check (LDPC) codes. We develop a subsequent verification\nprotocol with the use of $\\epsilon$-universal hash functions, which allows\nverifying the identity between the keys with a certain probability.", "category": "quant-ph" }, { "text": "Foundations of quantum mechanics: decoherence and interpretation: In this paper we review Castagnino's contributions to the foundations of\nquantum mechanics. First, we recall his work on quantum decoherence in closed\nsystems, and the proposal of a general framework for decoherence from which the\nphenomenon acquires a conceptually clear meaning. Then, we introduce his\ncontribution to the hard field of the interpretation of quantum mechanics: the\nmodal-Hamiltonian interpretation solves many of the interpretive problems of\nthe theory, and manifests its physical relevance in its application to many\ntraditional models of the practice of physics. In the third part of this work\nwe describe the ontological picture of the quantum world that emerges from the\nmodal-Hamiltonian interpretation, stressing the philosophical step toward a\ndeep understanding of the reference of the theory.", "category": "quant-ph" }, { "text": "Optimization at the Interface of Unitary and Non-unitary Quantum\n Operations in PCOAST: The Pauli-based Circuit Optimization, Analysis and Synthesis Toolchain\n(PCOAST) was recently introduced as a framework for optimizing quantum\ncircuits. It converts a quantum circuit to a Pauli-based graph representation\nand provides a set of optimization subroutines to manipulate that internal\nrepresentation as well as methods for re-synthesizing back to a quantum\ncircuit. In this paper, we focus on the set of subroutines which look to\noptimize the PCOAST graph in cases involving unitary and non-unitary operations\nas represented by nodes in the graph. This includes reduction of node cost and\nnode number in the presence of preparation nodes, reduction of cost for\nClifford operations in the presence of preparations, and measurement cost\nreduction using Clifford operations and the classical remapping of measurement\noutcomes. These routines can also be combined to amplify their effectiveness.\n We evaluate the PCOAST optimization subroutines using the Intel Quantum SDK\non examples of the Variational Quantum Eigensolver (VQE) algorithm. This\nincludes synthesizing a circuit for the simultaneous measurement of a mutually\ncommuting set of Pauli operators. We find for such measurement circuits the\noverall average ratio of the maximum theoretical number of two-qubit gates to\nthe actual number of two-qubit gates used by our method to be 7.91.", "category": "quant-ph" }, { "text": "The origin of anticorrelation for photon bunching on a beam splitter: The Copenhagen interpretation has been long-lasted, whose core concepts are\nin the Heisenberg's uncertainty principle and nonlocal correlation of EPR. The\nsecond-order anticorrelation on a beam splitter represents these phenomena\nwhere it cannot be achieved classically. Here, the anticorrelation of\nnonclassicality on a beam splitter is interpreted in a purely coherence manner.\nUnlike a common belief in a particle nature of photons, the anticorrelation\nroots in pure wave nature of coherence optics, where quantum superposition\nbetween two input fields plays a key role. This interpretation may intrigue a\nfundamental question of what nonclassicality should be and pave a road to\ncoherence-based quantum information.", "category": "quant-ph" }, { "text": "Enhanced absorption Hanle effect on the Fg=F->Fe=F+1 closed transitions: We analyse the Hanle effect on a closed $F_g\\to F_e=F_g+1$ transition. Two\nconfigurations are examined, for linear- and circular-polarized laser\nradiation, with the applied magnetic field collinear to the laser light\nwavevector. We describe the peculiarities of the Hanle signal for\nlinearly-polarized laser excitation, characterized by narrow bright resonances\nat low laser intensities. The mechanism behind this effect is identified, and\nnumerical solutions for the optical Bloch equations are presented for different\ntransitions.", "category": "quant-ph" }, { "text": "Autonomous quantum thermal machine for generating steady-state\n entanglement: We discuss a simple quantum thermal machine for the generation of\nsteady-state entanglement between two interacting qubits. The machine is\nautonomous in the sense that it uses only incoherent interactions with thermal\nbaths, but no source of coherence or external control. By weakly coupling the\nqubits to thermal baths at different temperatures, inducing a heat current\nthrough the system, steady-state entanglement is generated far from thermal\nequilibrium. Finally, we discuss two possible implementations, using\nsuperconducting flux qubits or a semiconductor double quantum dot. Experimental\nprospects for steady-state entanglement are promising in both systems.", "category": "quant-ph" }, { "text": "Information bound for entropy production from the detailed fluctuation\n theorem: Fluctuation theorems impose fundamental bounds in the statistics of the\nentropy production, with the second law of thermodynamics being the most\nfamous. Using information theory, we quantify the information of entropy\nproduction and find an upper tight bound as a function of its mean from the\nstrong detailed fluctuation theorem. The bound is given in terms of a maximal\ndistribution, a member of the exponential family with nonlinear argument. We\nshow that the entropy produced by heat transfer using a bosonic mode at weak\ncoupling reproduces the maximal distribution in a limiting case. The upper\nbound is extended to the continuous domain and verified for the heat transfer\nusing a levitated nanoparticle. Finally, we show that a composition of qubit\nswap engines satisfies a particular case of the maximal distribution regardless\nof its size.", "category": "quant-ph" }, { "text": "Quantum walks can find a marked element on any graph: We solve an open problem by constructing quantum walks that not only detect\nbut also find marked vertices in a graph. In the case when the marked set $M$\nconsists of a single vertex, the number of steps of the quantum walk is\nquadratically smaller than the classical hitting time $HT(P,M)$ of any\nreversible random walk $P$ on the graph. In the case of multiple marked\nelements, the number of steps is given in terms of a related quantity\n$HT^+(\\mathit{P,M})$ which we call extended hitting time.\n Our approach is new, simpler and more general than previous ones. We\nintroduce a notion of interpolation between the random walk $P$ and the\nabsorbing walk $P'$, whose marked states are absorbing. Then our quantum walk\nis simply the quantum analogue of this interpolation. Contrary to previous\napproaches, our results remain valid when the random walk $P$ is not\nstate-transitive. We also provide algorithms in the cases when only\napproximations or bounds on parameters $p_M$ (the probability of picking a\nmarked vertex from the stationary distribution) and $HT^+(\\mathit{P,M})$ are\nknown.", "category": "quant-ph" }, { "text": "Purity through Factorisation: We give a construction that identifies the collection of pure processes (i.e.\nthose which are deterministic, or without randomness) within a theory\ncontaining both pure and mixed processes. Working in the framework of symmetric\nmonoidal categories, we define a pure subcategory. This definition arises\nelegantly from the categorical notion of a weak factorisation system. Our\nconstruction gives the expected result in several examples, both quantum and\nclassical.", "category": "quant-ph" }, { "text": "Non-Gaussian superradiant transition via three-body ultrastrong coupling: We introduce a class of quantum optical Hamiltonian characterized by\nthree-body couplings, and propose a circuit-QED scheme based on\nstate-of-the-art technology that implements the considered model. Unlike\ntwo-body light-matter interactions, this three-body coupling Hamiltonian is\nexclusively composed of terms which do not conserve the particle number. We\nexplore the three-body ultrastrong coupling regime, showing the emergence of a\nsuperradiant phase transition which is of first order, is characterized by the\nbreaking of a $\\mathbb{Z}_2\\times \\mathbb{Z}_2$ symmetry and has a strongly\nnon-Gaussian nature. Indeed, in contrast to what is observed in any\ntwo-body-coupling model, in proximity of the transition the ground state\nexhibits a divergent coskewness, i.e., quantum correlations that cannot be\ncaptured within semiclassical and Gaussian approximations. Furthermore, we\ndemonstrate the robustness of our findings by including dissipative processes\nin the model, showing that the steady-state of the system inherits from the\nground states the most prominent features of the transition.", "category": "quant-ph" }, { "text": "The Measurement Problem: Decoherence and Convivial Solipsism: The problem of measurement is often considered as an inconsistency inside the\nquantum formalism. Many attempts to solve (or to dissolve) it have been made\nsince the inception of quantum mechanics. The form of these attempts depends on\nthe philosophical position that their authors endorse. I will review some of\nthem and analyze their relevance. The phenomenon of decoherence is often\npresented as a solution lying inside the pure quantum formalism and not\ndemanding any particular philosophical assumption. Nevertheless, a widely\ndebated question is to decide between two different interpretations. The first\none is to consider that the decoherence process has the effect to actually\nproject a superposed state into one of its classically interpretable component,\nhence doing the same job as the reduction postulate. For the second one,\ndecoherence is only a way to show why no macroscopic superposed state can be\nobserved, so explaining the classical appearance of the macroscopic world,\nwhile the quantum entanglement between the system, the apparatus and the\nenvironment never disappears. In this case, explaining why only one single\ndefinite outcome is observed remains to do. In this paper, I examine the\narguments that have been given for and against both interpretations and defend\na new position, the \"Convivial Solipsism\" , according to which the outcome that\nis observed is relative to the observer, different but in close parallel to the\nEverett's interpretation and sharing also some similarities with Rovelli's\nrelational interpretation and quantum bayesianism. I also show how \"Convivial\nSolipsism\" can help getting a new standpoint about the EPR paradox providing a\nway out of the standard dilemma that is having to choose between abandoning\neither realism or locality.", "category": "quant-ph" }, { "text": "Calculating the distance from an electronic wave function to the\n manifold of Slater determinants through the geometry of Grassmannians: The set of all electronic states that can be expressed as a single Slater\ndeterminant forms a submanifold, isomorphic to the Grassmannian, of the\nprojective Hilbert space of wave functions. We explored this fact by using\ntools of Riemannian geometry of Grassmannians as described by Absil et. al\n[Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to a\nSlater determinant that is critical point of the overlap function with a\ncorrelated wave function. This algorithm can be applied to quantify the\nentanglement or correlation of a wave function. We show that this algorithm is\nequivalent to the Newton method using the standard parametrization of Slater\ndeterminants by orbital rotations, but it can be more efficiently implemented\nbecause the orbital basis used to express the correlated wave function is kept\nfixed throughout the iterations. We present the equations of this method for a\ngeneral configuration interaction wave function and for a wave function with up\nto double excitations over a reference determinant. Applications of this\nalgorithm to selected electronic systems are also presented and discussed.", "category": "quant-ph" }, { "text": "Environment-assisted holonomic quantum maps: Holonomic quantum computation uses non-Abelian geometric phases to realize\nerror resilient quantum gates. Nonadiabatic holonomic gates are particularly\nsuitable to avoid unwanted decoherence effects, as they can be performed at\nhigh speed. By letting the computational system interact with a structured\nenvironment, we show that the scope of error resilience of nonadiabatic\nholonomic gates can be widened to include systematic parameter errors. Our\nscheme maintains the geometric properties of the evolution and results in an\nenvironment-assisted holonomic quantum map that can mimic the effect of a\nholonomic gate. We demonstrate that the sensitivity to systematic errors can be\nreduced in a proof-of-concept spin-bath model.", "category": "quant-ph" }, { "text": "Measurement of conditional phase shifts for quantum logic: Measurements of the birefringence of a single atom strongly coupled to a\nhigh-finesse optical resonator are reported, with nonlinear phase shifts\nobserved for intracavity photon number much less than one. A proposal to\nutilize the measured conditional phase shifts for implementing quantum logic\nvia a quantum-phase gate (QPG) is considered. Within the context of a simple\nmodel for the field transformation, the parameters of the \"truth table\" for the\nQPG are determined.", "category": "quant-ph" }, { "text": "Modulation and Measurement of Time-Energy Entangled Photons: We describe a proof-of-principal experiment demonstrating a Fourier technique\nfor measuring the shape of biphoton wavepackets. The technique is based on the\nuse of synchronously driven fast modulators and slow (integrating) detectors.", "category": "quant-ph" }, { "text": "Quantum Teleportation through Noisy Channels with Multi-Qubit GHZ States: We investigate two-party quantum teleportation through noisy channels for\nmulti-qubit Greenberger-Horne-Zeilinger (GHZ) states and find which state loses\nless quantum information in the process. The dynamics of states is described by\nthe master equation with the noisy channels that lead to the quantum channels\nto be mixed states. We analytically solve the Lindblad equation for $n$-qubit\nGHZ states $n\\in\\{4,5,6\\}$ where Lindblad operators correspond to the Pauli\nmatrices and describe the decoherence of states. Using the average fidelity we\nshow that 3GHZ state is more robust than $n$GHZ state under most noisy\nchannels. However, $n$GHZ state preserves same quantum information with respect\nto EPR and 3GHZ states where the noise is in $x$ direction in which the\nfidelity remains unchanged. We explicitly show that Jung ${\\it et\\, al.}$\nconjecture [Phys. Rev. A ${\\bf 78}$, 012312 (2008)], namely, \"average fidelity\nwith same-axis noisy channels are in general larger than average fidelity with\ndifferent-axis noisy channels\" is not valid for 3GHZ and 4GHZ states.", "category": "quant-ph" }, { "text": "Quantum frequency estimation with trapped ions and atoms: We discuss strategies for quantum enhanced estimation of atomic transition\nfrequencies with ions stored in Paul traps or neutral atoms trapped in optical\nlattices. We show that only marginal quantum improvements can be achieved using\nstandard Ramsey interferometry in the presence of collective dephasing, which\nis the major source of noise in relevant experimental setups. We therefore\nanalyze methods based on decoherence free subspaces and prove that quantum\nenhancement can readily be achieved even in the case of significantly imperfect\nstate preparation and faulty detections.", "category": "quant-ph" }, { "text": "Decoherence and Quantum Error Correction for Quantum Computing and\n Communications: Quantum technologies have shown immeasurable potential to effectively solve\nseveral information processing tasks such as prime number factorization,\nunstructured database search or complex macromolecule simulation. As a result\nof such capability to solve certain problems that are not classically\ntractable, quantum machines have the potential revolutionize the modern world\nvia applications such as drug design, process optimization, unbreakable\ncommunications or machine learning. However, quantum information is prone to\nsuffer from errors caused by the so-called decoherence, which describes the\nloss in coherence of quantum states associated to their interactions with the\nsurrounding environment. This decoherence phenomenon is present in every\nquantum information task, be it transmission, processing or even storage of\nquantum information. Consequently, the protection of quantum information via\nquantum error correction codes (QECC) is of paramount importance to construct\nfully operational quantum computers. Understanding environmental decoherence\nprocesses and the way they are modeled is fundamental in order to construct\neffective error correction methods capable of protecting quantum information.\nIn this thesis, the nature of decoherence is studied and mathematically\nmodelled; and QECCs are designed and optimized so that they exhibit better\nerror correction capabilities.", "category": "quant-ph" }, { "text": "Qubit-induced phonon blockade as a signature of quantum behavior in\n nanomechanical resonators: The observation of quantized nanomechanical oscillations by detecting\nfemtometer-scale displacements is a significant challenge for experimentalists.\nWe propose that phonon blockade can serve as a signature of quantum behavior in\nnanomechanical resonators. In analogy to photon blockade and Coulomb blockade\nfor electrons, the main idea for phonon blockade is that the second phonon\ncannot be excited when there is one phonon in the nonlinear oscillator. To\nrealize phonon blockade, a superconducting quantum two-level system is coupled\nto the nanomechanical resonator and is used to induce the phonon\nself-interaction. Using Monte Carlo simulations, the dynamics of the induced\nnonlinear oscillator is studied via the Cahill-Glauber $s$-parametrized\nquasiprobability distributions. We show how the oscillation of the resonator\ncan occur in the quantum regime and demonstrate how the phonon blockade can be\nobserved with currently accessible experimental parameters.", "category": "quant-ph" }, { "text": "Adaptive Continuous Homodyne Phase Estimation Using Robust\n Fixed-Interval Smoothing: Adaptive homodyne estimation of a continuously evolving optical phase using\ntime-symmetric quantum smoothing has been demonstrated experimentally to\nprovide superior accuracy in the phase estimate compared to adaptive or\nnonadaptive estimation using filtering alone. Here, we illustrate how the\nmean-square error in the adaptive phase estimate may be further reduced below\nthe standard quantum limit for the stochastic noise process considered by using\na Rauch-Tung-Striebel smoother as the estimator, alongwith an optimal Kalman\nfilter in the feedback loop. Further, the estimation using smoothing can be\nmade robust to uncertainties in the underlying parameters of the noise process\nmodulating the system phase to be estimated. This has been done using a robust\nfixed-interval smoother designed for uncertain systems satisfying a certain\nintegral quadratic constraint.", "category": "quant-ph" }, { "text": "Kraus representation for maps and master equation in spin star model\n with layered environment: Quantum operations are usually defined as completely positive (CP), trace\npreserving (TP) maps on quantum states, and can be represented by operator-sum\nor Kraus representations. In this paper, we calculate operator-sum\nrepresentation and master equation of an exactly solvable dynamic of one-qubit\nopen system in layered environment . On the other hand, we obtain exact\nNakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the\nmaps. Finally, we study a simple example to consider the relation between CP\nmaps and initial quantum correlation and show that vanishing initial quantum\ncorrelation is not necessary for CP maps.", "category": "quant-ph" }, { "text": "Stochastic approximate state conversion for entanglement and general\n quantum resource theories: Quantum resource theories provide a mathematically rigorous way of\nunderstanding the nature of various quantum resources. An important problem in\nany quantum resource theory is to determine how quantum states can be converted\ninto each other within the physical constraints of the theory. The standard\napproach to this problem is to study approximate or probabilistic\ntransformations. Very few results have been presented on the intermediate\nregime between probabilistic and approximate transformations. Here, we\ninvestigate this intermediate regime, providing limits on both, the fidelity\nand the probability of state transitions. We derive limitations on the\ntransformations, which are valid in all quantum resource theories, by providing\nbounds on the maximal transformation fidelity for a given transformation\nprobability. We also show that the deterministic version of this bound can be\napplied for drawing limitations on the manipulation of quantum channels, which\ngoes beyond the previously known bounds of channel manipulations. As an\napplication, we show that the fidelity between Popescu-Rohrlich box and an\nisotropic box cannot increase via any locality preserving superchannel.\nFurthermore, we completely solve the question of stochastic-approximate state\ntransformations via local operations and classical communications in the case\nof pure bipartite entangled state transformations of arbitrary dimensions and\ntwo-qubit entanglement for arbitrary final states, when starting from a pure\nbipartite state.", "category": "quant-ph" }, { "text": "Exceptional and regular spectra of a generalized Rabi model: We study the spectrum of the generalized Rabi model in which co- and\ncounter-rotating terms have different coupling strengths. It is also equivalent\nto the model of a two-dimensional electron gas in a magnetic field with Rashba\nand Dresselhaus spin-orbit couplings. Like in case of the Rabi model, the\nspectrum of the generalized Rabi model consists of the regular and the\nexceptional parts. The latter is represented by the energy levels which cross\nat certain parameters' values which we determine explicitly. The wave functions\nof these exceptional states are given by finite order polynomials in the\nBargmann representation. The roots of these polynomials satisfy a Bethe ansatz\nequation of the Gaudin type. At the exceptional points the model is therefore\nquasi-exactly solvable. An analytical approximation is derived for the regular\npart of the spectrum in the weak- and strong-coupling limits. In particular, in\nthe strong-coupling limit the spectrum consists of two quasi-degenerate\nequidistant ladders.", "category": "quant-ph" }, { "text": "Circuit-based Modular Implementation of Quantum Ghost Imaging: Efforts on enhancing the ghost imaging speed and quality are intensified when\nthe debate around the nature of ghost imaging (quantum vs. classical) is\nsuspended for a while. Accordingly, most of the studies these years in the\nfield fall into the improvement regarding these two targets by utilizing the\ndifferent imaging mediums. Nevertheless, back to the raging debate occurred but\nwith different focus, to overcome the inherent difficulties in the classical\nimaging domain, if we are able to utilize the superiority that quantum\ninformation science offers us, the ghost imaging experiment may be implemented\nmore practically. In this study, a quantum circuit implementation of ghost\nimaging experiment is proposed, where the speckle patterns and phase mask are\nencoded by utilizing the quantum representation of images. To do this, we\nformulated several quantum models, i.e. quantum accumulator, quantum\nmultiplier, and quantum divider. We believe this study will provide a new\nimpetus to explore the implementation of ghost imaging using quantum computing\nresources.", "category": "quant-ph" }, { "text": "Quantum conditional operations: An essential element of classical computation is the \"if-then\" construct,\nthat accepts a control bit and an arbitrary gate, and provides conditional\nexecution of the gate depending on the value of the controlling bit. On the\nother hand, quantum theory prevents the existence of an analogous universal\nconstruct accepting a control qubit and an arbitrary quantum gate as its input.\nNevertheless, there are controllable sets of quantum gates for which such a\nconstruct exists. Here we provide a necessary and sufficient condition for a\nset of unitary transformations to be controllable, and we give a complete\ncharacterization of controllable sets in the two dimensional case. This result\nreveals an interesting connection between the problem of controllability and\nthe problem of extracting information from an unknown quantum gate while using\nit.", "category": "quant-ph" }, { "text": "A Fidelity Susceptibility Approach to Quantum Annealing of NP-hard\n problems: The computational complexity conjecture of NP $\\nsubseteq$ BQP implies that\nthere should be an exponentially small energy gap for Quantum Annealing (QA) of\nNP-hard problems. We aim to verify how this computation originated gapless\npoint could be understood based on physics, using the quantum Monte Carlo\nmethod. As a result, we found a phase transition detectable only by the\ndivergence of fidelity susceptibility. The exponentially small gapless points\nof each instance are all located in the phase found in this study, which\nsuggests that this phase transition is the physical cause of the failure of QA\nfor NP-hard problems.", "category": "quant-ph" }, { "text": "Polaron formation in a spin chain by measurement-induced imaginary\n Zeeman field: We present a high-rate projective measurement-based approach for controlling\nnon-unitary evolution of a quantum chain of interacting spins. In this\napproach, we demonstrate that local measurement of a single external spin\ncoupled to the chain can produce a spin polaron, which remains stable after the\nend of the measurement. This stability results from the fact that the Hilbert\nspace of the chain contains a subspace of non-decaying states, stable during\nthe nonunitary evolution. These states determine the resulting final state of\nthe chain and long-term shape of the polaron. In addition to formation of the\nspin polarons, the presented measurement protocol can be used for distillation\nof non-decaying states from an initial superposition or mixture.", "category": "quant-ph" }, { "text": "An updated analysis of satellite quantum-key distribution missions: Quantum key distribution (QKD) is a cryptographic method enabling two parties\nto establish a private encryption key. The range of communication of\nground-based QKD is limited to an order of 100km, due to in-fibre attenuations\nand atmospheric losses, and the development of quantum repeaters remains\ntechnologically challenging. While trusted-node links make communication over\nlarge distances possible, satellite-QKD is required for communication over\nglobal distances. By using satellites equipped with high-quality optical links,\nsatellite-QKD can achieve ultra-long-distance quantum communication in the\n1000-km range. The significant potential of satellite-QKD for the creation of\nglobal quantum networks thus makes it a particularly interesting field of\nresearch. In this analysis, we begin with an overview of the technical\nparameters of performing satellite-QKD, including infrastructure and protocols.\nWe continue with a high-level summary of advancements in satellite-QKD by\nanalysing past, present and proposed satellite-QKD missions and initiatives\naround the world. We conclude by discussing the technical challenges currently\nfaced in satellite-QKD, which can be tackled through future research in this\narea.", "category": "quant-ph" }, { "text": "Generating a 4-photon Tetrahedron State: Towards Simultaneous\n Super-sensitivity to Non-commuting Rotations: It is often thought that the super-sensitivity of a quantum state to an\nobservable comes at the cost of a decreased sensitivity to other non-commuting\nobservables. For example, a squeezed state squeezed in position quadrature is\nsuper-sensitive to position displacements, but very insensitive to momentum\ndisplacements. This misconception was cleared with the introduction of the\ncompass state, a quantum state equally super-sensitive to displacements in\nposition and momentum. When looking at quantum states used to measure spin\nrotations, N00N states are known to be more advantageous than classical methods\nas long as they are aligned to the rotation axis. When considering the\nestimation of a rotation with unknown direction and amplitude, a certain class\nof states stands out with interesting properties. These states are equally\nsensitive to rotations around any axis, are second-order unpolarized, and can\npossess the rotational properties of platonic solids in particular dimensions.\nImportantly, these states are optimal for simultaneously estimating the three\nparameters describing a rotation. In the asymptotic limit, estimating all d\nparameters describing a transformation simultaneously rather than sequentially\ncan lead to a reduction of the appropriately-weighted sum of the measured\nparameters' variances by a factor of d. We report the experimental creation and\ncharacterization of the lowest-dimensional such state, which we call the\n\"tetrahedron state\" due to its tetrahedral symmetry. This tetrahedron state is\ncreated in the symmetric subspace of four optical photons' polarization in a\nsingle spatial and temporal mode, which behaves as a spin-2 particle. While\nimperfections due to the hardware limit the performance of our method, we argue\nthat better technology can improve our method to the point of outperforming any\nother existing strategy in per-photon comparisons.", "category": "quant-ph" }, { "text": "Squeezed Light and Entangled Images from Four-Wave-Mixing in Hot\n Rubidium Vapor: Entangled multi-spatial-mode fields have interesting applications in quantum\ninformation, such as parallel quantum information protocols, quantum computing,\nand quantum imaging. We study the use of a nondegenerate four-wave mixing\nprocess in rubidium vapor at 795 nm to demonstrate generation of\nquantum-entangled images. Owing to the lack of an optical resonator cavity, the\nfour-wave mixing scheme generates inherently multi-spatial-mode output fields.\nWe have verified the presence of entanglement between the multi-mode beams by\nanalyzing the amplitude difference and the phase sum noise using a dual\nhomodyne detection scheme, measuring more than 4 dB of squeezing in both cases.\nThis paper will discuss the quantum properties of amplifiers based on\nfour-wave-mixing, along with the multi mode properties of such devices.", "category": "quant-ph" }, { "text": "Entanglement Generation is Not Necessary for Optimal Work Extraction: We consider reversible work extraction from identical quantum batteries. From\nan ensemble of individually passive states, work can be produced only via\nglobal unitary (and thus entangling) operations. However, we show here that\nthere always exists a method to extract all possible work without creating any\nentanglement, at the price of generically requiring more operations (i.e.\nadditional time). We then study faster methods to extract work and provide a\nquantitative relation between the amount of generated multipartite entanglement\nand extractable work. Our results suggest a general relation between\nentanglement generation and the power of work extraction.", "category": "quant-ph" }, { "text": "Quantum Storage of Heralded Single Photons in a Praseodymium Doped\n Crystal: We report on experiments demonstrating the reversible mapping of heralded\nsingle photons to long lived collective optical atomic excitations stored in a\nPr$^{3+}$:Y$_2$SiO$_5$ crystal. A cavity-enhanced spontaneous down-conversion\nsource is employed to produce widely non-degenerate narrow-band ($\\approx\n2\\,\\mathrm{MHz}$) photon-pairs. The idler photons, whose frequency is\ncompatible with telecommunication optical fibers, are used to herald the\ncreation of the signal photons, compatible with the Pr$^{3+}$ transition. The\nsignal photons are stored and retrieved using the atomic frequency comb\nprotocol. We demonstrate storage times up to $4.5\\,\\mathrm{\\mu s}$ while\npreserving non-classical correlations between the heralding and the retrieved\nphoton. This is more than 20 times longer than in previous realizations in\nsolid state devices, and implemented in a system ideally suited for the\nextension to spin-wave storage.", "category": "quant-ph" }, { "text": "Simultaneous weak measurement of non-commuting observables: In contrast to a projective quantum measurement in which the system is\nprojected onto an eigenstate of the measured operator, in a weak measurement\nthe system is only weakly perturbed while only partial information on the\nmeasured observable is obtained. A full description of such measurement should\ndescribe the measurement protocol and provide an explicit form of the\nmeasurement operator that transform the quantum state to its post measurement\nform. A simultaneous measurement of non-commuting observables cannot be\nprojective, however the strongest possible such measurement can be defined as\nproviding their values at the smallest uncertainty limit. Starting with the\nArthurs and Kelly (AK) protocol for such measurement of position and momentum,\nwe derive a systematic extension to a corresponding weak measurement along\nthree steps: First, a plausible form of the weak measurement operator analogous\nto the Gaussian Kraus operator often used to model a weak measurement of a\nsingle observable is obtained by projecting a na\\\"ive extension (valid for\ncommuting observable) onto the corresponding Gabor space. Second, we show that\nthe so obtained set of measurement operators satisfies the normalization\ncondition for the probability to obtain given values of the position and\nmomentum in the weak measurement operation, namely that this set constitutes a\npositive operator valued measure (POVM) in the position-momentum space.\nFinally, we show that the so-obtained measurement operator corresponds to a\ngeneralization of the AK measurement protocol in which the initial detector\nwavefunctions is suitable broadened.", "category": "quant-ph" }, { "text": "The Hybrid Topological Longitudinal Transmon Qubit: We introduce a new hybrid qubit consisting of a Majorana qubit interacting\nwith a transmon longitudinally coupled to a resonator. To do so, we equip the\nlongitudinal transmon qubit with topological quasiparticles, supported by an\narray of heterostructure nanowires, and derive charge- and phase-based\ninteractions between the Majorana qubit and the resonator and transmon degrees\nof freedom. Inspecting the charge coupling, we demonstrate that the Majorana\nself-charging can be eliminated by a judicious choice of charge offset, thereby\nmaintaining the Majorana degeneracy regardless of the quasiparticles spatial\narrangement and parity configuration. We perform analytic and numerical\ncalculations to derive the effective qubit-qubit interaction elements and\ndiscuss their potential utility for state readout and quantum error correction.\nFurther, we find that select interactions depend strongly on the overall\nsuperconducting parity, which may provide a direct mechanism to characterize\ndeleterious quasiparticle poisoning processes.", "category": "quant-ph" }, { "text": "Realization of generalized quantum searching using nuclear magnetic\n resonance: According to the theoretical results, the quantum searching algorithm can be\ngeneralized by replacing the Walsh-Hadamard(W-H) transform by almost any\nquantum mechanical operation. We have implemented the generalized algorithm\nusing nuclear magnetic resonance techniques with a solution of chloroform\nmolecules. Experimental results show the good agreement between theory and\nexperiment.", "category": "quant-ph" }, { "text": "Proposed experiment for testing quantum contextuality with neutrons: We show that an experimental demonstration of quantum contextuality using 2\ndegrees of freedom of single neutrons based on a violation of an inequality\nderived from the Peres-Mermin proof of the Kochen-Specker theorem would be more\nconclusive than those obtained from previous experiments involving pairs of\nions [M. A. Rowe et al., Nature (London) 409, 791 (2001)] and single neutron\n[Y. Hasegawa et al., Nature (London) 425, 45 (2003)] based on violations of\nClauser-Horne-Shimony-Holt-like inequalities.", "category": "quant-ph" }, { "text": "A new interpretation of superposition, entanglement, and measurement in\n quantum mechanics: We present a new interpretation of the terms superposition, entanglement, and\nmeasurement that appear in quantum mechanics. We hypothesize that the structure\nof the wave function for a quantum system at the sub-Planck scale has a\ndeterministic cyclic structure. Each cycle comprises a sequential succession of\nthe eigenstates that comprise a given wave function. Between unitary operations\nor measurements on the wave function, the sequential arrangement of the current\neigenstates chosen by the system is immaterial, but once chosen it remains\nfixed until another unitary operation or measurement changes the wave function.\nThe probabilistic aspect of quantum mechanics is interpreted by hypothesizing a\nmeasurement mechanism which acts instantaneously but the instant of measurement\nis chosen randomly by the classical measuring apparatus over a small but finite\ninterval from the time the measurement apparatus is activated. At the instant\nthe measurement is made, the wave function irrevocably collapses to a new state\n(erasing some of the past quantum information) and continues from thereon in\nthat state till changed by a unitary operation or a new measurement.", "category": "quant-ph" }, { "text": "Franck-Condon factors by counting perfect matchings of graphs with loops: We show that the Franck-Condon Factor (FCF) associated to a transition\nbetween initial and final vibrational states in two different potential energy\nsurfaces, having $N$ and $M$ vibrational quanta, respectively, is equivalent to\ncalculating the number of perfect matchings of a weighted graph with loops that\nhas $P = N+M$ vertices. This last quantity is the loop hafnian of the\n(symmetric) adjacency matrix of the graph which can be calculated in $O(P^3\n2^{P/2})$ steps. In the limit of small numbers of vibrational quanta per normal\nmode our loop hafnian formula significantly improves the speed at which FCFs\ncan be calculated. Our results more generally apply to the calculation of the\nmatrix elements of a bosonic Gaussian unitary between two multimode Fock states\nhaving $N$ and $M$ photons in total and provide a useful link between certain\ncalculations of quantum chemistry, quantum optics and graph theory.", "category": "quant-ph" }, { "text": "Quantum filter for a non-Markovian single qubit system: In this paper, a quantum filter for estimating the states of a non-Markovian\nqubit system is presented in an augmented Markovian system framework including\nboth the qubit system of interest and multi-ancillary systems for representing\nthe internal modes of the non-Markovian environment. The colored noise\ngenerated by the multi-ancillary systems disturbs the qubit system via a direct\ninteraction. The resulting non-Markovian dynamics of the qubit is determined by\na memory kernel function arising from the dynamics of the ancillary system. In\nprinciple, colored noise with arbitrary power spectrum can be generated by a\ncombination of Lorentzian noises. Hence, the quantum filter can be constructed\nfor the qubit disturbed by arbitrary colored noise and the conditional state of\nthe qubit system can be obtained by tracing out the multi-ancillary systems. An\nillustrative example is given to show the non-Markovian dynamics of the qubit\nsystem with Lorentzian noise.", "category": "quant-ph" }, { "text": "Quasi-exactly solvable quartic Bose Hamiltonians: We consider Hamiltonians, which are even polynomials of the forth order with\nthe respect to Bose operators. We find subspaces, preserved by the action of\nHamiltonian These subspaces, being finite-dimensional, include, nonetheless,\nstates with an \\QTR{it}{infinite} number of quasi-particles, corresponding to\nthe original Bose operators. The basis functions look rather simple in the\ncoherent state representation and are expressed in terms of the degenerate\nhypergeometric function with respect to the complex variable labeling the\nrepresentation. In some particular degenerate cases they turn (up to the power\nfactor) into the trigonometric or hyperbolic functions, Bessel functions or\ncombinations of the exponent and Hermit polynomials. We find explicitly the\nrelationship between coefficients at different powers of Bose operators that\nensure quasi-exact solvability of Hamiltonian.", "category": "quant-ph" }, { "text": "Transformation of quantum states using uniformly controlled rotations: We consider a unitary transformation which maps any given state of an\n$n$-qubit quantum register into another one. This transformation has\napplications in the initialization of a quantum computer, and also in some\nquantum algorithms. Employing uniformly controlled rotations, we present a\nquantum circuit of $2^{n+2}-4n-4$ CNOT gates and $2^{n+2}-5$ one-qubit\nelementary rotations that effects the state transformation. The complexity of\nthe circuit is noticeably lower than the previously published results.\nMoreover, we present an analytic expression for the rotation angles needed for\nthe transformation.", "category": "quant-ph" }, { "text": "Zeno Dynamics and Distinguishability of Quantum States: According to the quantum Zeno effect, the frequent observations of a system\ncan dramatically slow down its dynamical evolution. We show that the Zeno\ndynamics is the result of projective measurements among quantum states which\nare indistinguishable. The physical time scale of the problem is provided by\nthe Cramer-Rao lower bound, which measure the distinguishability of states\nalong a path in the Hilbert space. We finally show that the Zeno dynamics with\nparticle entangled states might require quite smaller measurement intervals\nthan classically correlated states, and propose a realistic interferometric\nexperiment to test the prediction.", "category": "quant-ph" }, { "text": "Quantum speedup for twin support vector machines: We devise new quantum algorithms that exponentially speeds up the training\nand prediction procedures of twin support vector machines (TSVM). To train\nTSVMs using quantum methods, we demonstrate how to prepare the desired input\nstates according to classical data, and these states are used in the quantum\nalgorithm for the system of linear equations. In the prediction process, we\nemploy a quantum circuit to estimate the distances from a new sample to the\nhyperplanes and then make a decision. The proposed quantum algorithms can learn\ntwo non-parallel hyperplanes and classify a new sample by comparing the\ndistances from the sample to the two hyperplanes in $O(\\log mn)$ time, where\n$m$ is the sample size and $n$ is the dimension of each data point. In\ncontrast, the corresponding classical algorithm requires polynomial time for\nboth the training and prediction procedures.", "category": "quant-ph" }, { "text": "Analysis of Lyapunov Control for Hamiltonian Quantum Systems: We present detailed analysis of the convergence properties and effectiveness\nof Lyapunov control design for bilinear Hamiltonian quantum systems based on\nthe application of LaSalle's invariance principle and stability analysis from\ndynamical systems and control theory. For a certain class of Hamiltonians,\nstrong convergence results can be obtained for both pure and mixed state\nsystems. The control Hamiltonians for realistic physical systems, however,\ngenerally do not fall in this class. It is shown that the effectiveness of\nLyapunov control design in this case is significantly diminished.", "category": "quant-ph" }, { "text": "Bell states diagonal entanglement witnesses: It has been shown that finding generic Bell states diagonal entanglement\nwitnesses (BDEW) for $d_{1}\\otimes d_{2}\\otimes ....\\otimes d_{n}$ systems\nexactly reduces to a linear programming if the feasible region be a polygon by\nitself and approximately obtains via linear programming if the feasible region\nis not a polygon. Since solving linear programming for generic case is\ndifficult, the multi-qubits, $2\\otimes N$ and $3 \\otimes 3$ systems for the\nspecial case of generic BDEW for some particular choice of their parameters\nhave been considered. In the rest of this paper we obtain the optimal non\ndecomposable entanglement witness for $3 \\otimes 3$ system for some particular\nchoice of its parameters. By proving the optimality of the well known reduction\nmap and combining it with the optimal and non-decomposable 3 $\\otimes$ 3 BDEW\n(named critical entanglement witnesses) the family of optimal and\nnon-decomposable 3 $\\otimes$ 3 BDEW have also been obtained. Using the\napproximately critical entanglement witnesses, some 3 $\\otimes$ 3 bound\nentangled states are so detected. So the well known Choi map as a particular\ncase of the positive map in connection with this witness via Jamiolkowski\nisomorphism has been considered which approximately is obtained via linear\nprogramming.", "category": "quant-ph" }, { "text": "Limit distributions of three-state quantum walks: the role of coin\n eigenstates: We analyze two families of three-state quantum walks which show the\nlocalization effect. We focus on the role of the initial coin state and its\ncoherence in controlling the properties of the quantum walk. In particular, we\nshow that the description of the walk simplifies considerably when the initial\ncoin state is decomposed in the basis formed by the eigenvectors of the coin\noperator. This allows us to express the limit distributions in a much more\nconvenient form. Consequently, striking features which are hidden in the\nstandard basis description are easily identified. Moreover, the dependence of\nmoments of the position distribution on the initial coin state can be analyzed\nin full detail. In particular, we find that in the eigenvector basis the even\nmoments and the localization probability at the origin depend only on\nincoherent combination of probabilities. In contrast, odd moments and\nlocalization outside the origin are affected by the coherence of the initial\ncoin state.", "category": "quant-ph" }, { "text": "Enhanced quantum transport in chiral quantum walks: Quantum transport across discrete structures is a relevant topic of solid\nstate physics and quantum information science, which can be suitably studied in\nthe context of continuous-time quantum walks. The addition of phases degrees of\nfreedom, leading to chiral quantum walks, can also account for directional\ntransport on graphs with loops. We discuss criteria for quantum transport and\nstudy the enhancement that can be achieved with chiral quantum walks on\nchain-like graphs, exploring different topologies for the chain units and\noptimizing over the phases. We select three candidate structures with optimal\nperformance and investigate their transport behaviour with Krylov reduction.\nWhile one of them can be reduced to a weighted line with minor couplings\nmodulation, the other two are truly chiral quantum walks, with enhanced\ntransport probability over long chain structures.", "category": "quant-ph" }, { "text": "Spectral filtering in quantum Y-junction: We examine scattering properties of singular vertex of degree $n=2$ and\n$n=3$, taking advantage of a new form of representing the vertex boundary\ncondition, which has been devised to approximate a singular vertex with finite\npotentials. We show that proper identification of $\\delta$ and $\\delta'$\ncomponents in the connection condition between outgoing lines enables the\ndesigning of quantum spectral branch-filters.", "category": "quant-ph" }, { "text": "Adaptive quantum state estimation for two optical point sources: In classical optics, there is a well-known resolution limit, called\nRayleigh's curse, in the separation of two incoherent optical sources in close\nproximity. Recently, Tsang et al. revealed that this difficulty may be\ncircumvented in the framework of quantum theory. Following their work, various\nestimation methods have been proposed to overcome Rayleigh's curse, but none of\nthem enables us to estimate the positions of two point sources simultaneously\nbased on single-photon measurements with high accuracy. In this study, we\npropose a method to simultaneously estimate the positions of two point sources\nwith the highest accuracy using adaptive quantum state estimation scheme.", "category": "quant-ph" }, { "text": "The role of coherence in the non-equilibrium thermodynamics of quantum\n systems: Exploiting the relative entropy of coherence, we isolate the coherent\ncontribution in the energetics of a driven non-equilibrium quantum system. We\nprove that a division of the irreversible work can be made into a coherent and\nincoherent part, which provides an operational criterion for quantifying the\ncoherent contribution in a generic non-equilibrium transformation on a closed\nquantum system. We then study such a contribution in two physical models of a\ndriven qubit and kicked rotor. In addition, we also show that coherence\ngeneration is connected to the non-adiabaticity of a processes, for which it\ngives the dominant contribution for slow-enough transformation. The amount of\ngenerated coherence in the energy eigenbasis is equivalent to the change in\ndiagonal entropy, and here we show that it fulfills a fluctuation theorem.", "category": "quant-ph" }, { "text": "Operator equations and Moyal products -- metrics in quasi-hermitian\n quantum mechanics: The Moyal product is used to cast the equation for the metric of a\nnon-hermitian Hamiltonian in the form of a differential equation. For\nHamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact\nequation. Solving this equation in perturbation theory recovers known results.\nExplicit criteria for the hermiticity and positive definiteness of the metric\nare formulated on the functional level.", "category": "quant-ph" }, { "text": "Quantum State Discrimination Using the Minimum Average Number of Copies: In the task of discriminating between nonorthogonal quantum states from\nmultiple copies, the key parameters are the error probability and the resources\n(number of copies) used. Previous studies have considered the task of\nminimizing the average error probability for fixed resources. Here we introduce\na new state discrimination task: minimizing the average resources for a fixed\nadmissible error probability. We show that this new task is not performed\noptimally by previously known strategies, and derive and experimentally test a\ndetection scheme that performs better.", "category": "quant-ph" }, { "text": "Proceedings 13th International Conference on Quantum Physics and Logic: This volume contains the proceedings of the 13th International Conference on\nQuantum Physics and Logic (QPL 2016), which was held June 6-10, 2016 at the\nUniversity of Strathclyde. QPL is a conference that brings together researchers\nworking on mathematical foundations of quantum physics, quantum computing, and\nrelated areas, with a focus on structural perspectives and the use of logical\ntools, ordered algebraic and category-theoretic structures, formal languages,\nsemantical methods, and other computer science techniques applied to the study\nof physical behaviour in general.", "category": "quant-ph" }, { "text": "Reinforcement-learning based matterwave interferometer in a shaken\n optical lattice: We demonstrate the design of a matterwave interferometer to measure\nacceleration in one dimension with high precision. The system we base this on\nconsists of ultracold atoms in an optical lattice potential created by\ninterfering laser beams. Our approach uses reinforcement learning, a branch of\nmachine learning, that generates the protocols needed to realize lattice-based\nanalogs of optical components including a beam splitter, a mirror, and a\nrecombiner. The performance of these components is evaluated by comparison with\ntheir optical analogs. The interferometer's sensitivity to acceleration is\nquantitatively evaluated using a Bayesian statistical approach. We find the\nsensitivity to surpass that of standard Bragg interferometry, demonstrating the\nfuture potential for this design methodology.", "category": "quant-ph" }, { "text": "Numerical treatment of interfaces in Quantum Mechanics: In this article we develop a numerical scheme to deal with interfaces between\ntouching numerical grids when solving Schr\\\"o{}dinger equation. In order to\npass the information among grids we use the values of the fields only at the\ncontact point between them. Surprisingly we obtain a convergent methods which\nis third order accurate with respect to the spatial resolution. In test cases,\nat the minimal resolution needed to describe correctly the waves, the error of\nthis approximation is similar to that of a homogeneous (centered differences\neverywhere) scheme with three points stencil, that is a sixth order finite\ndifference operator. The semi-discrete approximation preserves the norm and\nuses standard finite difference operators satisfying summation by parts. For\nthe time integrator we use a semi-implicit IMEX Runge Kutta method.", "category": "quant-ph" }, { "text": "Collapse Models and Perceptual Processes: Theories including a collapse mechanism have been presented various years\nago. They are based on a modification of standard quantum mechanics in which\nnonlinear and stochastic terms are added to the evolution equation. Their\nprincipal merits derive from the fact that they are mathematically precise\nschemes accounting, on the basis of a unique universal dynamical principle,\nboth for the quantum behavior of microscopic systems as well as for the\nreduction associated to measurement processes and for the classical behavior of\nmacroscopic objects. Since such theories qualify themselves not as new\ninterpretations but as modifications of the standard theory they can be, in\nprinciple, tested against quantum mechanics. Recently, various investigations\nidentifying possible crucial test have been discussed. In spite of the extreme\ndifficulty to perform such tests it seems that recent technological\ndevelopments allow at least to put precise limits on the parameters\ncharacterizing the modifications of the evolution equation. Here we will simply\nmention some of the recent investigations in this direction, while we will\nmainly concentrate our attention to the way in which collapse theories account\nfor definite perceptual process. The differences between the case of reductions\ninduced by perceptions and those related to measurement procedures by means of\nstandard macroscopic devices will be discussed. On this basis, we suggest a\nprecise experimental test of collapse theories involving conscious observers.\nWe make plausible, by discussing in detail a toy model, that the modified\ndynamics can give rise to quite small but systematic errors in the visual\nperceptual process.", "category": "quant-ph" }, { "text": "GPU-accelerated simulations of quantum annealing and the quantum\n approximate optimization algorithm: We study large-scale applications using a GPU-accelerated version of the\nmassively parallel J\\\"ulich universal quantum computer simulator (JUQCS--G).\nFirst, we benchmark JUWELS Booster, a GPU cluster with 3744 NVIDIA A100 Tensor\nCore GPUs. Then, we use JUQCS--G to study the relation between quantum\nannealing (QA) and the quantum approximate optimization algorithm (QAOA). We\nfind that a very coarsely discretized version of QA, termed approximate quantum\nannealing (AQA), performs surprisingly well in comparison to the QAOA. It can\neither be used to initialize the QAOA, or to avoid the costly optimization\nprocedure altogether. Furthermore, we study the scaling of the success\nprobability when using AQA for problems with 30 to 40 qubits. We find that the\ncase with the largest discretization error scales most favorably, surpassing\nthe best result obtained from the QAOA.", "category": "quant-ph" }, { "text": "Predicting human-generated bitstreams using classical and quantum models: A school of thought contends that human decision making exhibits quantum-like\nlogic. While it is not known whether the brain may indeed be driven by actual\nquantum mechanisms, some researchers suggest that the decision logic is\nphenomenologically non-classical. This paper develops and implements an\nempirical framework to explore this view. We emulate binary decision-making\nusing low width, low depth, parameterized quantum circuits. Here, entanglement\nserves as a resource for pattern analysis in the context of a simple\nbit-prediction game. We evaluate a hybrid quantum-assisted machine learning\nstrategy where quantum processing is used to detect correlations in the\nbitstreams while parameter updates and class inference are performed by\nclassical post-processing of measurement results. Simulation results indicate\nthat a family of two-qubit variational circuits is sufficient to achieve the\nsame bit-prediction accuracy as the best traditional classical solution such as\nneural nets or logistic autoregression. Thus, short of establishing a provable\n\"quantum advantage\" in this simple scenario, we give evidence that the\nclassical predictability analysis of a human-generated bitstream can be\nachieved by small quantum models.", "category": "quant-ph" }, { "text": "Quantum Operation Time Reversal: The dynamics of an open quantum system can be described by a quantum\noperation, a linear, complete positive map of operators. Here, I exhibit a\ncompact expression for the time reversal of a quantum operation, which is\nclosely analogous to the time reversal of a classical Markov transition matrix.\nSince open quantum dynamics are stochastic, and not, in general, deterministic,\nthe time reversal is not, in general, an inversion of the dynamics. Rather, the\nsystem relaxes towards equilibrium in both the forward and reverse time\ndirections. The probability of a quantum trajectory and the conjugate, time\nreversed trajectory are related by the heat exchanged with the environment.", "category": "quant-ph" }, { "text": "Satellite Quantum Communications: Fundamental Bounds and Practical\n Security: Satellite quantum communications are emerging within the panorama of quantum\ntechnologies as a more effective strategy to distribute completely-secure keys\nat very long distances, therefore playing an important role in the architecture\nof a large-scale quantum network. In this work, we apply and extend recent\nresults in free-space quantum communications to determine the ultimate limits\nat which secret (and entanglement) bits can be distributed via satellites. Our\nstudy is comprehensive of the various practical scenarios, encompassing both\ndownlink and uplink configurations, with satellites at different altitudes and\nzenith angles. It includes effects of diffraction, extinction, background noise\nand fading, due to pointing errors and atmospheric turbulence (appropriately\ndeveloped for slant distances). Besides identifying upper bounds, we also\ndiscuss lower bounds, i.e., achievable rates for key generation and\nentanglement distribution. In particular, we study the composable finite-size\nsecret key rates that are achievable by protocols of continuous variable\nquantum key distribution, for both downlink and uplink, showing the feasibility\nof this approach for all configurations. Finally, we present a study with a\nsun-synchronous satellite, showing that its key distribution rate is able to\noutperform a ground chain of ideal quantum repeaters.", "category": "quant-ph" }, { "text": "Statistical link between Bell nonlocality and uncertainty relations: Bell nonlocality and uncertainty relations are distinct features of quantum\ntheory from classical physics. Bell nonlocality concerns the correlation\nstrength among local observables on different quantum particles, whereas the\nuncertainty relations set the lower bound of the sum or product of the variance\nsquare of observables. Here we establish the statistical link between these two\nquantum characters using the Aharonov-Vaidman identity. Therein, the upper\nbounds of Bell-type inequalities are expressed in terms of the product of the\nlocal sum of the variance square. On the other hand, instead of evaluating\nlocal uncertainty relations, the uncertainty relations on two or more quantum\nsystems are upper-bounded by the amount of Bell nonlocality therein.", "category": "quant-ph" }, { "text": "Fidelity balance in quantum operations: I derive a tight bound between the quality of estimating the state of a\nsingle copy of a $d$-level system, and the degree the initial state has to be\naltered in course of this procedure. This result provides a complete analytical\ndescription of the quantum mechanical trade-off between the information gain\nand the quantum state disturbance expressed in terms of mean fidelities. I also\ndiscuss consequences of this bound for quantum teleportation using nonmaximally\nentangled states.", "category": "quant-ph" }, { "text": "Maximal violation of the Ardehali's inequality of $n$ qubits: In this paper, we characterize the maximal violation of Ardehali's inequality\nof $n$ qubits by showing that GHZ's states and the states obtained from them by\nlocal unitary transformations are the unique states that maximally violate the\nArdehali's inequalities. This concludes that Ardehali's inequalities can be\nused to characterize maximally entangled states of $n$ qubits, as the same as\nMermin's and Bell-Klyshko's inequalities.", "category": "quant-ph" }, { "text": "Continuous Variable Quantum MNIST Classifiers: In this paper, classical and continuous variable (CV) quantum neural network\nhybrid multiclassifiers are presented using the MNIST dataset. The combination\nof cutoff dimension and probability measurement method in the CV model allows a\nquantum circuit to produce output vectors of size equal to n raised to the\npower of n where n represents cutoff dimension and m, the number of qumodes.\nThey are then translated as one-hot encoded labels, padded with an appropriate\nnumber of zeros. The total of eight different classifiers are built using\n2,3,...,8 qumodes, based on the binary classifier architecture proposed in\nContinuous variable quantum neural networks. The displacement gate and the Kerr\ngate in the CV model allow for the bias addition and nonlinear activation\ncomponents of classical neural networks to quantum. The classifiers are\ncomposed of a classical feedforward neural network, a quantum data encoding\ncircuit, and a CV quantum neural network circuit. On a truncated MNIST dataset\nof 600 samples, a 4 qumode hybrid classifier achieves 100% training accuracy.", "category": "quant-ph" }, { "text": "Quantum dynamics of disordered arrays of interacting superconducting\n qubits: signatures of quantum collective states: We study theoretically the collective quantum dynamics occurring in various\ninteracting superconducting qubits arrays (SQAs) in the presence of a spread of\nindividual qubit frequencies. The interaction is provided by mutual inductive\ncoupling between adjacent qubits (short-range Ising interaction) or inductive\ncoupling to a low-dissipative resonator (long-range exchange interaction). In\nthe absence of interaction the Fourier transform of temporal correlation\nfunction of the total polarization ($z$-projection of the total spin), i.e. the\ndynamic susceptibility $C(\\omega)$, demonstrates a set of sharp small magnitude\nresonances corresponding to the transitions of individual superconducting\nqubits. We show that even a weak interaction between qubits can overcome the\ndisorder with a simultaneous formation of the collective excited states. This\ncollective behavior manifests itself by a single large resonance in\n$C(\\omega)$. In the presence of a weak non-resonant microwave photon field in\nthe low-dissipative resonator, the positions of dominant resonances depend on\nthe number of photons, i.e. the collective ac Stark effect. Coupling of an SQA\nto the transmission line allows a straightforward experimental access of the\ncollective states in microwave transmission experiments and, at the same time,\nto employ SQAs as sensitive single-photon detectors.", "category": "quant-ph" }, { "text": "Time-Reversal-Symmetric Single-Photon Wave Packets for Free-Space\n Quantum Communication: Readout and retrieval processes are proposed for efficient, high-fidelity\nquantum state transfer between a matter qubit, encoded in the level structure\nof a single atom or ion, and a photonic qubit, encoded in a\ntime-reversal-symmetric single-photon wave packet. They are based on\ncontrolling spontaneous photon emission and absorption of a matter qubit on\ndemand in free space by stimulated Raman adiabatic passage. As these processes\ndo not involve mode selection by high-finesse cavities or photon transport\nthrough optical fibers, they offer interesting perspectives as basic building\nblocks for free-space quantum-communication protocols.", "category": "quant-ph" }, { "text": "Classical and Quantum Ensembles via Multiresolution. I. BBGKY Hierarchy: A fast and efficient numerical-analytical approach is proposed for modeling\ncomplex behaviour in the BBGKY hierarchy of kinetic equations. We construct the\nmultiscale representation for hierarchy of reduced distribution functions in\nthe variational approach and multiresolution decomposition in polynomial tensor\nalgebras of high-localized states. Numerical modeling shows the creation of\nvarious internal structures from localized modes, which are related to\nlocalized or chaotic type of behaviour and the corresponding patterns\n(waveletons) formation. The localized pattern is a model for energy confinement\nstate (fusion) in plasma.", "category": "quant-ph" }, { "text": "Experimental Quantum Simulation of Entanglement in Many-body Systems: We employ a nuclear magnetic resonance (NMR) quantum information processor to\nsimulate the ground state of an XXZ spin chain and measure its NMR analog of\nentanglement, or pseudo-entanglement. The observed pseudo-entanglement for a\nsmall-size system already displays singularity, a signature which is\nqualitatively similar to that in the thermodynamical limit across quantum phase\ntransitions, including an infinite-order critical point. The experimental\nresults illustrate a successful approach to investigate quantum correlations in\nmany-body systems using quantum simulators.", "category": "quant-ph" }, { "text": "Experimental Simulation of Loop Quantum Gravity on a Photonic Chip: The unification of general relativity and quantum theory is one of the\nfascinating problems of modern physics. One leading solution is Loop Quantum\nGravity (LQG). Simulating LQG may be important for providing predictions which\ncan then be tested experimentally. However, such complex quantum simulations\ncannot run efficiently on classical computers, and quantum computers or\nsimulators are needed. Here, we experimentally demonstrate quantum simulations\nof spinfoam amplitudes of LQG on an integrated photonics quantum processor. We\nsimulate a basic transition of LQG and show that the derived spinfoam vertex\namplitude falls within 4% error with respect to the theoretical prediction,\ndespite experimental imperfections. We also discuss how to generalize the\nsimulation for more complex transitions, in realistic experimental conditions,\nwhich will eventually lead to a quantum advantage demonstration as well as\nexpand the toolbox to investigate LQG.", "category": "quant-ph" }, { "text": "A Size-Consistent Wave-function Ansatz Built from Statistical Analysis\n of Orbital Occupations: Direct approaches to the quantum many-body problem suffer from the so-called\n\"curse of dimensionality\": the number of parameters needed to fully specify the\nexact wavefunction grows exponentially with increasing system size. This\nmotivates the develop of accurate, but approximate, ways to parametrize the\nwavefunction, including methods like couple cluster theory and correlator\nproduct states (CPS). Recently, there has been interest in approaches based on\nmachine learning both direct applications of neural network architecture and\nthe combinations of conventional wavefunction parametrizations with various\nBoltzmann machines. While all these methods can be exact in principle, they are\nusually applied with only a polynomial number of parameters, limiting their\napplicability. This research's objective is to present a fresh approach to\nwavefunction parametrization that is size-consistent, rapidly convergent, and\nrobust numerically. Specifically, we propose a hierarchical ansatz that\nconverges rapidly (with respect to the number of least-squares optimization).\nThe general utility of this approach is verified by applying it to\nuncorrelated, weakly-correlated, and strongly-correlated systems, including\nsmall molecules and the one-dimensional Hubbard model.", "category": "quant-ph" }, { "text": "Graph-theoretical Bounds on the Entangled Value of Non-local Games: We introduce a novel technique to give bounds to the entangled value of\nnon-local games. The technique is based on a class of graphs used by Cabello,\nSeverini and Winter in 2010. The upper bound uses the famous Lov\\'asz theta\nnumber and is efficiently computable; the lower one is based on the quantum\nindependence number, which is a quantity used in the study of\nentanglement-assisted channel capacities and graph homomorphism games.", "category": "quant-ph" }, { "text": "Two-photon interference with true thermal light: Two-photon interference and \"ghost\" imaging with entangled light have\nattracted much attention since the last century because of the novel features\nsuch as non-locality and sub-wavelength effect. Recently, it has been found\nthat pseudo-thermal light can mimic certain effects of entangled light. We\nreport here the first observation of two-photon interference with true thermal\nlight.", "category": "quant-ph" }, { "text": "The Goldilocks model of separable, zero-range, few-body interactions in\n one-dimensional harmonic traps: This article introduces the \"Goldilocks model\" for a few repulsively\ninteracting particles trapped in a one-dimensional harmonic well and provides\nexact solutions for the three-particle case. The Goldilocks model shares\nfeatures with two other well-known systems, the Calogero model and the\ncontact-interaction model, and coincides with them in limiting cases. However,\nthose models have purely two-body interactions whereas this model has\nintrinsically few-body interactions. Comparing these three models provides\nclarifying distinctions among the properties of symmetry, separability and\nintegrability. The model's analytic solutions provide a useful basis to improve\napproximation schemes, especially near the unitary limit of hard-core contact\ninteractions.", "category": "quant-ph" }, { "text": "Quantum metrology with entangled coherent states: We present an improved phase estimation scheme employing entangled coherent\nstates and demon- strate that the states give the smallest variance in the\nphase parameter in comparison to NOON, BAT and \"optimal\" states under perfect\nand lossy conditions. As these advantages emerge for very modest particle\nnumbers, the optical version of entangled coherent state metrology is\nachievable with current technology.", "category": "quant-ph" }, { "text": "Quantum Metrology with Indefinite Causal Order: We address the study of quantum metrology enhanced by indefinite causal\norder, demonstrating a quadratic advantage in the estimation of the product of\ntwo average displacements in a continuous variable system. We prove that no\nsetup where the displacements are probed in a fixed order can have\nroot-mean-square error vanishing faster than the Heisenberg limit 1/N, where N\nis the number of displacements contributing to the average. In stark contrast,\nwe show that a setup that probes the displacements in a superposition of two\nalternative orders yields a root-mean-square error vanishing with\nsuper-Heisenberg scaling 1/N^2. This result opens up the study of new\nmeasurement setups where quantum processes are probed in an indefinite order,\nand suggests enhanced tests of the canonical commutation relations, with\npotential applications to quantum gravity.", "category": "quant-ph" }, { "text": "Atomistic and orthoatomistic effect algebras: We characterize atomistic effect algebras, prove that a weakly orthocomplete\nArchimedean atomic effect algebra is orthoatomistic and present an example of\nan orthoatomistic orthomodular poset that is not weakly orthocomplete.", "category": "quant-ph" }, { "text": "Graphs whose normalized Laplacian matrices are separable as density\n matrices in quantum mechanics: Recently normalized Laplacian matrices of graphs are studied as density\nmatrices in quantum mechanics. Separability and entanglement of density\nmatrices are important properties as they determine the nonclassical behavior\nin quantum systems. In this note we look at the graphs whose normalized\nLaplacian matrices are separable or entangled. In particular, we show that the\nnumber of such graphs is related to the number of 0-1 matrices that are line\nsum symmetric and to the number of graphs with at least one vertex of degree 1.", "category": "quant-ph" }, { "text": "Phase-space formulation of quantum mechanics and quantum state\n reconstruction for physical systems with Lie-group symmetries: We present a detailed discussion of a general theory of phase-space\ndistributions, introduced recently by the authors [J. Phys. A {\\bf 31}, L9\n(1998)]. This theory provides a unified phase-space formulation of quantum\nmechanics for physical systems possessing Lie-group symmetries. The concept of\ngeneralized coherent states and the method of harmonic analysis are used to\nconstruct explicitly a family of phase-space functions which are postulated to\nsatisfy the Stratonovich-Weyl correspondence with a generalized traciality\ncondition. The symbol calculus for the phase-space functions is given by means\nof the generalized twisted product. The phase-space formalism is used to study\nthe problem of the reconstruction of quantum states. In particular, we consider\nthe reconstruction method based on measurements of displaced projectors, which\ncomprises a number of recently proposed quantum-optical schemes and is also\nrelated to the standard methods of signal processing. A general group-theoretic\ndescription of this method is developed using the technique of harmonic\nexpansions on the phase space.", "category": "quant-ph" }, { "text": "Optical response of a misaligned and suspended Fabry-Perot cavity: The response to a probe laser beam of a suspended, misaligned and detuned\noptical cavity is examined. A five degree of freedom model of the fluctuations\nof the longitudinal and transverse mirror coordinates is presented. Classical\nand quantum mechanical effects of radiation pressure are studied with the help\nof the optical stiffness coefficients and the signals provided by an FM\nsideband technique and a quadrant detector, for generic values of the product\n$\\varpi \\tau $ of the fluctuation frequency times the cavity round trip. A\nsimplified version is presented for the case of small misalignments. Mechanical\nstability, mirror position entanglement and ponderomotive squeezing are\naccommodated in this model. Numerical plots refer to cavities under test at the\nso-called Pisa LF facility.", "category": "quant-ph" }, { "text": "Entangled-state generation and Bell inequality violations in\n nanomechanical resonators: We investigate theoretically the conditions under which a multi-mode\nnanomechanical resonator, operated as a purely mechanical parametric\noscillator, can be driven into highly nonclassical states. We find that when\nthe device can be cooled to near its ground state, and certain mode matching\nconditions are satisfied, it is possible to prepare distinct resonator modes in\nquantum entangled states that violate Bell inequalities with homodyne\nquadrature measurements. We analyze the parameter regimes for such Bell\ninequality violations, and while experimentally challenging, we believe that\nthe realization of such states lies within reach. This is a re-imagining of a\nquintessential quantum optics experiment by using phonons that represent\ntangible mechanical vibrations.", "category": "quant-ph" }, { "text": "A Quantum Computational Semantics for Epistemic Logical Operators. Part\n II: Semantics: By using the abstract structures investigated in the first Part of this\narticle, we develop a semantics for an epistemic language, which expresses\nsentences like \"Alice knows that Bob does not understand that PI is\nirrational\". One is dealing with a holistic form of quantum computational\nsemantics, where entanglement plays a fundamental role, thus, the meaning of a\nglobal expression determines the contextual meanings of its parts, but\ngenerally not the other way around. The epistemic situations represented in\nthis semantics seem to reflect some characteristic limitations of the real\nprocesses of acquiring information. Since knowledge is not generally closed\nunder logical consequence, the unpleasant phenomenon of logical omniscience is\nhere avoided.", "category": "quant-ph" }, { "text": "Coupled Cluster Downfolding Methods: the effect of double commutator\n terms on the accuracy of ground-state energies: Downfolding coupled cluster (CC) techniques have recently been introduced\ninto quantum chemistry as a tool for the dimensionality reduction of the\nmany-body quantum problem. As opposed to earlier formulations in physics and\nchemistry based on the concept of effective Hamiltonians, the appearance of the\ndownfolded Hamiltonians is a natural consequence of the single-reference\nexponential parametrization of the wave function. In this paper, we discuss the\nimpact of higher-order terms originating in double commutators. In analogy to\nprevious studies, we consider the case when only one- and two-body interactions\nare included in the downfolded Hamiltonians. We demonstrate the efficiency of\nthe many-body expansions involving single and double commutators for the\nunitary extension of the downfolded Hamiltonians on the example of the\nberyllium atom, and bond-breaking processes in the Li2 and H2O molecules. For\nthe H2O system, we also analyze energies obtained with downfolding procedures\nas functions of the active space size.", "category": "quant-ph" }, { "text": "Statistical dynamics of a non-Abelian anyonic quantum walk: We study the single particle dynamics of a mobile non-Abelian anyon hopping\naround many pinned anyons on a surface. The dynamics is modelled by a discrete\ntime quantum walk and the spatial degree of freedom of the mobile anyon becomes\nentangled with the fusion degrees of freedom of the collective system. Each\nquantum trajectory makes a closed braid on the world lines of the particles\nestablishing a direct connection between statistical dynamics and quantum link\ninvariants. We find that asymptotically a mobile Ising anyon becomes so\nentangled with its environment that its statistical dynamics reduces to a\nclassical random walk with linear dispersion in contrast to particles with\nAbelian statistics which have quadratic dispersion.", "category": "quant-ph" }, { "text": "Continuous-time quantum walks on dynamical percolation graphs: We address continuous-time quantum walks on graphs in the presence of time-\nand space-dependent noise. Noise is modeled as generalized dynamical\npercolation, i.e. classical time-dependent fluctuations affecting the tunneling\namplitudes of the walker. In order to illustrate the general features of the\nmodel, we review recent results on two paradigmatic examples: the dynamics of\nquantum walks on the line and the effects of noise on the performances of\nquantum spatial search on the complete and the star graph. We also discuss\nfuture perspectives, including extension to many-particle quantum walk, to\nnoise model for on-site energies and to the analysis of different noise\nspectra. Finally, we address the use of quantum walks as a quantum probe to\ncharacterize defects and perturbations occurring in complex, classical and\nquantum, networks.", "category": "quant-ph" }, { "text": "Double exceptional points generated by the strong imaginary coupling of\n a non-Hermitian Hamiltonian in an optical microcavity: Exceptional points (EPs) have recently attracted considerable attention in\nthe study of non-Hermitian systems and in applications such as sensors and mode\nswitching. In particular, nontrivial topological structures of EPs have been\nstudied intensively in relation to encircling EPs. Thus, EP generation is\ncurrently an important issue in several fields. To generate multiple EPs,\nmultiple levels or composite physical systems have been employed with Hermitian\ncouplings. In this study, we generate multiple EPs on two-level systems in a\nsingle microcavity by adopting the non-Hermitian coupling of a non-Hermitian\nHamiltonian under the imaginary (dominant) coupling. The topological structures\nof Riemann surfaces generated by non-Hermitian coupling exhibit features that\nare different from those of Riemann surfaces generated by Hermitian coupling.\nThe features of these topological structures of Riemann surfaces were verified\nby encircling multiple EPs and using a Riemann sphere.", "category": "quant-ph" }, { "text": "Eigenvalues and Low Energy Eigenvectors of Quantum Many-Body Systems: I first give an overview of the thesis and Matrix Product States (MPS)\nrepresentation of quantum spin chains with an improvement on the conventional\nnotation.\n The rest of this thesis is divided into two parts. The first part is devoted\nto eigenvalues of quantum many-body systems (QMBS). I introduce Isotropic\nEntanglement, which draws from various tools in random matrix theory and free\nprobability theory (FPT) to accurately approximate the eigenvalue distribution\nof QMBS on a line with generic interactions. Next, I discuss the energy\ndistribution of one particle hopping random Schr\\\"odinger operator in 1D from\nFPT in context of the Anderson model.\n The second part is devoted to ground states and gap of QMBS. I first give the\nnecessary background on frustration free (FF) Hamiltonians, real and imaginary\ntime evolution within MPS representation and a numerical implementation. I then\nprove the degeneracy and FF condition for quantum spin chains with generic\nlocal interactions, including corrections to our earlier assertions. I then\nsummarize my efforts in proving lower bounds for the entanglement of the ground\nstates, which includes some new results, with the hope that they inspire future\nwork resulting in solving the conjecture given therein. Next I discuss two\ninteresting measure zero examples where FF Hamiltonians are carefully\nconstructed to give unique ground states with high entanglement. One of the\nexamples (i.e., $d=4$) has not appeared elsewhere. In particular, we calculate\nthe Schmidt numbers exactly, entanglement entropies and introduce a novel\ntechnique for calculating the gap which may be of independent interest. The\nlast chapter elaborates on one of the measure zero examples (i.e., $d=3$) which\nis the first example of a FF translation-invariant spin-1 chain that has a\nunique highly entangled ground state and exhibits signatures of a critical\nbehavior.", "category": "quant-ph" }, { "text": "Spatial entanglement using a quantum walk on a many-body system: The evolution of a many-particle system on a one-dimensional lattice,\nsubjected to a quantum walk can cause spatial entanglement in the lattice\nposition, which can be exploited for quantum information/communication\npurposes. We demonstrate the evolution of spatial entanglement and its\ndependence on the quantum coin operation parameters, the number of particles\npresent in the lattice and the number of steps of quantum walk on the system.\nThus, spatial entanglement can be controlled and optimized using a\nmany-particle discrete-time quantum walk.", "category": "quant-ph" }, { "text": "Hybrid quantum linear equation algorithm and its experimental test on\n IBM Quantum Experience: We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd\n(HHL) algorithm for solving a system of linear equations. In our hybrid scheme,\na classical information feed-forward is required from the quantum phase\nestimation algorithm to reduce a circuit depth from the original HHL algorithm.\nIn this paper, we show that this hybrid algorithm is functionally identical to\nthe HHL algorithm under the assumption that the number of qubits used in\nalgorithms is large enough. In addition, it is experimentally examined with\nfour qubits in the IBM Quantum Experience setups, and the experimental results\nof our algorithm show higher accurate performance on specific systems of linear\nequations than that of the HHL algorithm.", "category": "quant-ph" }, { "text": "High-Fidelity Single-Shot Toffoli Gate via Quantum Control: A single-shot Toffoli, or controlled-controlled-NOT, gate is desirable for\nclassical and quantum information processing. The Toffoli gate alone is\nuniversal for reversible computing and, accompanied by the Hadamard gate, forms\na universal gate set for quantum computing. The Toffoli gate is also a key\ningredient for (non-topological) quantum error correction. Currently Toffoli\ngates are achieved by decomposing into sequentially implemented single- and\ntwo-qubit gates, which requires much longer times and yields lower overall\nfidelities compared to a single-shot implementation. We develop a\nquantum-control procedure to construct a single-shot Toffoli gate for three\nnearest-neighbor-coupled superconducting transmon systems such that the\nfidelity is 99.9% and is as fast as an entangling two-qubit gate under the same\nrealistic conditions. The gate is achieved by a non-greedy quantum control\nprocedure using our enhanced version of the Differential Evolution algorithm.", "category": "quant-ph" }, { "text": "Constructing higher-order topological states in higher dimension: Higher-order topological phase as a generalization of Berry phase attracts an\nenormous amount of research. The current theoretical models supporting\nhigher-order topological phases, however, cannot give the connection between\nlower and higher-order topological phases when extending the lattice from lower\nto higher dimensions. Here, we theoretically propose and experimentally\ndemonstrate a topological corner state constructed from the edge states in one\ndimensional lattice. The two-dimensional square lattice owns independent\nspatial modulation of coupling in each direction, and the combination of edge\nstates in each direction come up to the higher-order topological corner state\nin two-dimensional lattice, revealing the connection of topological phase in\nlower and higher dimensional lattices. Moreover, the topological corner states\nin two-dimensional lattice can also be viewed as the dimension-reduction from a\nfour-dimensional topological phase characterized by vector Chern number,\nconsidering two modulation phases as synthetic dimensions in Aubry-Andre-Harper\nmodel discussed as example here. Our work deeps the understanding to\ntopological phases breaking through the lattice dimension, and provides a\npromising tool constructing higher topological phases in higher dimensional\nstructures.", "category": "quant-ph" }, { "text": "Entanglement generation resonances in XY chains: We examine the maximum entanglement reached by an initially fully aligned\nstate evolving in an XY Heisenberg spin chain placed in a uniform transverse\nmagnetic field. Both the global entanglement between one qubit and the rest of\nthe chain and the pairwise entanglement between adjacent qubits is analyzed. It\nis shown that in both cases the maximum is not a monotonous decreasing function\nof the aligning field, exhibiting instead a resonant behavior for low\nanisotropies, with pronounced peaks (a total of [n/2] peaks in the global\nentanglement for an $n$-spin chain), whose width is proportional to the\nanisotropy and whose height remains finite in the limit of small anisotropy. It\nis also seen that the maximum pairwise entanglement is not a smooth function of\nthe field even in small finite chains, where it may exhibit narrow peaks above\nstrict plateaus. Explicit analytical results for small chains, as well as\ngeneral exact results for finite n-spin chains obtained through the\nJordan-Wigner mapping, are discussed.", "category": "quant-ph" }, { "text": "Revisiting the damped quantum harmonic oscillator: We reanalyse the quantum damped harmonic oscillator, introducing three less\nthan common features. These are (i) the use of a continuum model of the\nreservoir rather than an ensemble of discrete oscillators, (ii) an exact\ndiagonalisation of the Hamiltonian by adapting a technique pioneered by Fano,\nand (iii) the use of the thermofield technique for describing a finite\ntemperature reservoir. We recover in this way a number of well-known and some,\nperhaps, less familiar results. An example of the latter is an ab initio proof\nthat the oscillator relaxes to the mean-force Gibbs state. We find that special\ncare is necessary when comparing the damped oscillator with its undamped\ncounterpart as the former has two distinct natural frequencies, one associated\nwith short time evolution and the other with longer times.", "category": "quant-ph" }, { "text": "Quantum-state transfer from an ion to a photon: A quantum network requires information transfer between distant quantum\ncomputers, which would enable distributed quantum information processing and\nquantum communication. One model for such a network is based on the\nprobabilistic measurement of two photons, each entangled with a distant atom or\natomic ensemble, where the atoms represent quantum computing nodes. A second,\ndeterministic model transfers information directly from a first atom onto a\ncavity photon, which carries it over an optical channel to a second atom; a\nprototype with neutral atoms has recently been demonstrated. In both cases, the\ncentral challenge is to find an efficient transfer process that preserves the\ncoherence of the quantum state. Here, following the second scheme, we map the\nquantum state of a single ion onto a single photon within an optical cavity.\nUsing an ion allows us to prepare the initial quantum state in a deterministic\nway, while the cavity enables high-efficiency photon generation. The mapping\nprocess is time-independent, allowing us to characterize the interplay between\nefficiency and fidelity. As the techniques for coherent manipulation and\nstorage of multiple ions at a single quantum node are well established, this\nprocess offers a promising route toward networks between ion-based quantum\ncomputers.", "category": "quant-ph" }, { "text": "State of the art and prospects for quantum computing: This is a brief review of the experimental and theoretical quantum computing.\nThe hopes for eventually building a useful quantum computer rely entirely on\nthe so-called \"threshold theorem\". In turn, this theorem is based on a number\nof assumptions, treated as axioms, i.e. as being satisfied exactly. Since in\nreality this is not possible, the prospects of scalable quantum computing will\nremain uncertain until the required precision, with which these assumptions\nshould be approached, is established. Some related sociological aspects are\nalso discussed. .", "category": "quant-ph" }, { "text": "Two-player quantum games: When player strategies are via directional\n choices: We propose a scheme for a quantum game based on performing an EPR type\nexperiment and in which each player's spatial directional choices are\nconsidered as their strategies. A classical mixed-strategy game is recovered by\nrestricting the players' choices to specific spatial trajectories. We show that\nfor players' directional choices for which the Bell-CHSH inequality is\nviolated, the players' payoffs in the quantum game have no mapping within the\nclassical mixed-strategy game. The scheme provides a more direct link between\nclassical and quantum games.", "category": "quant-ph" }, { "text": "Defining the $p$-wave scattering volume in the presence of dipolar\n interactions: The definition of the scattering volume for $p$-wave collisions needs to be\ngeneralized in the presence of dipolar interactions for which the potential\ndecreases with the interparticle separation as $1/R^3$. Here, we propose a\ngeneralized definition of the scattering volume characterizing the short-range\ninteractions in odd-parity waves, obtained from an analysis of the $p$-wave\ncomponent of the two-body threshold wave function. Our approach uses an\nasymptotic model and introduces explicitly the anisotropic dipole-dipole\ninteraction, which governs the ultracold collision dynamics at long-range. The\nshort-range interactions, which are essential to describe threshold resonances,\nare taken into account by a single parameter which is determined by the\nfield-free $s$-wave scattering length.", "category": "quant-ph" }, { "text": "The Quantum State of Classical Matter I: Solids and Measurements: Using the kinematic constraints of classical bodies we construct the\nallowable wavefunctions corresponding to classical solids. These are shown to\nbe long lived metastable states that are qualitatively far from eigenstates of\nthe true Hamiltonian. Extensions of this give an explicit description of phonon\noscillations in terms of the wavefunction itself and some consequences for the\ngeneral validity of the quasiparticle picture are presented. An intrinsic\ntheory of quantum measurement naturally arises based on Schr\\\"{o}dinger\nevolution that is local, consistent with relativity and extends to the case of\nnoninertial and deformable measurement devices that can have time changing\ninternal properties. This theory agrees with the Born interpretation in the\nlimit of static measuring devices. Care is given to the transport of conserved\nquantities during measurement.", "category": "quant-ph" }, { "text": "Quantum-Logic Synthesis of Hermitian Gates: In this paper, the problem of synthesizing a general Hermitian quantum gate\ninto a set of primary quantum gates is addressed. To this end, an extended\nversion of the Jacobi approach for calculating the eigenvalues of Hermitian\nmatrices in linear algebra is considered as the basis of the proposed synthesis\nmethod. The quantum circuit synthesis method derived from the Jacobi approach\nand its optimization challenges are described. It is shown that the proposed\nmethod results in multiple-control rotation gates around the y axis,\nmultiple-control phase shift gates, multiple-control NOT gates and a middle\ndiagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Z\ngates. Using the proposed approach, it is shown how multiple-control U gates,\nwhere U is a single-qubit Hermitian quantum gate, can be implemented using a\nlinear number of elementary gates in terms of circuit lines with the aid of one\nauxiliary qubit in an arbitrary state.", "category": "quant-ph" }, { "text": "Decoherence of a Measure of Entanglement: We demonstrate by an explicit model calculation that the decay of\nentanglement of two two-state systems (two qubits) is governed by the product\nof the factors that measure the degree of decoherence of each of the qubits,\nsubject to independent sources of quantum noise. This demonstrates an important\nphysical property that separated open quantum systems can evolve quantum\nmechanically on time scales larger than the times for which they remain\nentangled.", "category": "quant-ph" }, { "text": "Unextendible maximally entangled bases and mutually unbiased bases in\n multipartite systems: We generalize the notion of unextendible maximally entangled basis from\nbipartite systems to multipartite quantum systems. It is proved that there do\nnot exist unextendible maximally entangled bases in three-qubit systems.\nMoreover,two types of unextendible maximally entangled bases are constructed in\ntripartite quantum systems and proved to be not mutually unbiased.", "category": "quant-ph" }, { "text": "Quantum Algorithms and Simulation for Parallel and Distributed Quantum\n Computing: A viable approach for building large-scale quantum computers is to interlink\nsmall-scale quantum computers with a quantum network to create a larger\ndistributed quantum computer. When designing quantum algorithms for such a\ndistributed quantum computer, one can make use of the added parallelization and\ndistribution abilities inherent in the system. An added difficulty to then\novercome for distributed quantum computing is that a complex control system to\norchestrate the various components is required. In this work, we aim to address\nthese issues. We explicitly define what it means for a quantum algorithm to be\ndistributed and then present various quantum algorithms that fit the\ndefinition. We discuss potential benefits and propose a high-level scheme for\ncontrolling the system. With this, we present our software framework called\nInterlin-q, a simulation platform that aims to simplify designing and verifying\nparallel and distributed quantum algorithms. We demonstrate Interlin-q by\nimplementing some of the discussed algorithms using Interlin-q and layout\nfuture steps for developing Interlin-q into a control system for distributed\nquantum computers.", "category": "quant-ph" }, { "text": "Entanglement-Enhanced Quantum Key Distribution: We present and analyze a quantum key distribution protocol based on sending\nentangled N-qubit states instead of single-qubit ones as in the trail-blazing\nscheme by Bennett and Brassard (BB84). Since the qubits are sent individually,\nan eavesdropper is limited to accessing them one by one. In an intercept-resend\nattack, this fundamental restriction allows one to make the eavesdropper's\ninformation on the transmitted key vanish if even one of the qubits is not\nintercepted. The implied upper bound 1/(2N) for Eve's information is further\nshown not to be the lowest since in the case N = 2, the information can be\nreduced to less than 30% of that in BB84. In general, the protocol is at least\nas secure as BB84.", "category": "quant-ph" }, { "text": "Experimental purification of coherent states: We propose a scheme for optimal Gaussian purification of coherent states from\nseveral imperfect copies. The proposal is experimentally demonstrated for the\ncase of two copies of a coherent state sent through independent noisy channels.\nOur purification protocol relies on only linear optics and an ancilla vacuum\nstate, rendering this approach an interesting alternative to the more complex\nprotocols of entanglement distillation and quantum error correction.", "category": "quant-ph" }, { "text": "Variational dynamics of the sub-Ohmic spin-boson model on the basis of\n multiple Davydov $\\mathrm{D}_1$ states: Dynamics of the sub-Ohmic spin-boson model is investigated by employing a\nmultitude of the Davydov D$_1$ trial states, also known as the multi-D$_1$\nAnsatz. Accuracy in dynamics simulations is improved significantly over the\nsingle D$_1$ Ansatz, especially in the weak system-bath coupling regime. The\nreliability of the multi-D$_1$ Ansatz for various coupling strengths and\ninitial conditions are also systematically examined, with results compared\nclosely with those of the hierarchy equations of motion and the path integral\nMonte Carlo approaches. In addition, a coherent-incoherent phase crossover in\nthe nonequilibrium dynamics is studied through the multi-D$_1$ Ansatz. The\nphase diagram is obtained with a critical point $s_{c}=0.4$. For $s_{c}