Quantum computers in phase space

Abstract

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier Transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to directly measure the Wigner function in a given phase space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm.

16 pages, 7 figures, to appear in Phys Rev A

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Cited by in corpus (89)

• Discrete phase space based on finite fields
• Hudson's Theorem for finite-dimensional quantum systems
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Quantum Process Tomography of the Quantum Fourier Transform
• Quasi-probability representations of quantum theory with applications to quantum information science
• Classicality in discrete Wigner functions
• Discrete Wigner functions and quantum computational speedup
• Wigner Functions for Arbitrary Quantum Systems
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Non-Gaussianity as a signature of a quantum theory of gravity
• Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
• Symmetric Informationally Complete Measurements of Arbitrary Rank
• Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
• Quantum phase space measurement and entanglement validation made easy
• Discrete Wigner functions and the phase space representation of quantum teleportation
• Non-negative Wigner functions in prime dimensions
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Fractal Weyl laws in discrete models of chaotic scattering
• Dephasing representation of quantum fidelity for general pure and mixed states
• Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects
• Phase-space approach to the study of decoherence in quantum walks
• Wigner phase space distribution as a wave function
• Decoherence induced by a chaotic environment: A quantum walker with a complex coin
• New Phase Space Formulations and Quantum Dynamics Approaches
• A quantum gate array can be programmed to evaluate the expectation value of any operator
• Distribution of resonances for open quantum maps
• Wigner tomography of multispin quantum states
• Quantum Computing of Quantum Chaos in the Kicked Rotator Model
• Mutually unbiased bases and discrete Wigner functions
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Extrema of discrete Wigner functions and applications
• Extended Cahill and Glauber formalism for finite dimensional spaces II. Applications in quantum tomography and quantum teleportation
• Wigner function for a particle in an infinite lattice
• Wigner distributions for finite dimensional quantum systems: An algebraic approach
• Quantum Computation of a Complex System : the Kicked Harper Model
• Quantum algorithms for phase space tomography
• Loschmidt Echo and the Local Density of States
• Continuous time quantum walks in phase space
• Spectra of phase point operators in odd prime dimensions and the extended Clifford group
• Spectral properties and classical decays in quantum open systems
• Quantum state tomography of a single electron spin in diamond with Wigner reconstruction
• Wigner function for discrete phase space: exorcising ghost images
• Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment
• Noise models for superoperators in the chord representation
• Stability of quantum motion in regular systems: a uniform semiclassical approach
• Entanglement-screening by nonlinear resonances
• Measurement of complete and continuous Wigner functions for discrete atomic systems
• Operational quasiprobabilities for qudits
• Discrete Wigner distribution for two qubits: a characterization of entanglement properties
• Quantum Fourier transform, Heisenberg groups and quasiprobability distributions
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Wigner distributions for finite state systems without redundant phase point operators
• Wigner separability entropy and complexity of quantum dynamics
• From the discrete Weyl -- Wigner formalism for symmetric ordering to a number -- phase Wigner function
• Multifractality of quantum wave functions in the presence of perturbations
• Optical experiment to test negative probability in context of quantum-measurement selection
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
• A dynamical point of view of Quantum Information: Wigner measures
• Direct Measurement of Kirkwood-Rihaczek distribution for spatial properties of coherent light beam
• Interference in discrete Wigner functions
• Phase diagram for the Grover algorithm with static imperfections
• Normalization procedure for relaxation studies in NMR quantum information processing
• Spectral functions and localization landscape theory in speckle potentials
• Finite quantum tomography via semidefinite programming
• Representation of superoperators in double phase space
• Quantum walk on a toral phase space
• Efficient computations of quantum canonical Gibbs state in phase space
• Phase-space representations of SIC-POVM fiducial states
• Transition probabilities and transition rates in discrete phase space
• A dynamical point of view of Quantum Information: entropy, pressure and Wigner measures
• Wigner distribution on a double cylinder phase space for studying quantum error correction protocol
• Quantum-classical correspondence on compact phase space
• Translations and reflections on the torus: Identities for discrete Wigner functions and transforms
• Relation between phase space coverage and entanglement for spin-1/2 systems
• Quantum tomography with wavelet transform in Banach space on Homogeneous space
• Phase space patterns of quantum transport on ordered and disordered networks
• Quantum mechanics in phase space: First order comparison between the Wigner and the Fermi function
• Bath-induced correlations in an infinite-dimensional Hilbert space
• The classical skeleton of open quantum chaotic maps
• Wigner formalism for a particle on an infinite lattice: dynamics and spin
• Grand Unification of All Discrete Wigner Functions on $d\times d$ Phase Space
• Quantum Mechanics on Periodic and Non-Periodic Lattices and Almost Unitary Schwinger Operators
• Short-Time Loschmidt Gap in Dynamical Systems with Critical Chaos
• Computing Quantum Mean Values in the Deep Chaotic Regime
• On the stabilizer complexity of Hawking radiation
• Discrete phase-space structures and Wigner functions for $N$ qubits
• Understanding Squeezed States of Light Through Wigner's Phase-Space
• From Fermat's last theorem to the quantum computer
• Towards Lagrangian approach to quantum computations (revised)