Quantum walks with quantum chaotic coins: Of the Loschmidt echo, classical limit and thermalization

Abstract

Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-body localization and coupled kicked rotors, and saturates to a value that depends on the relative coin and walker space dimensions. In a coin dominated scenario, the chaos can thermalize the quantum walk to typical random states such that the entanglement saturates at the Haar averaged Page value, unlike in a walker dominated case when atypical states seem to be produced.

References in corpus (40)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Average Entropy of a Subsystem
• Quantum random walks - an introductory overview
• Unbounded growth of entanglement in models of many-body localization
• Universal computation by quantum walk
• Many body localization in Heisenberg XXZ magnet in a random field
• Spatial search by quantum walk
• Dynamics of Loschmidt echoes and fidelity decay
• Universal slow growth of entanglement in interacting strongly disordered systems
• Universal quantum computation using the discrete time quantum walk
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Sub-Planck spots of Schroedinger cats and quantum decoherence
• Ergodic dynamics and thermalization in an isolated quantum system
• Average Entropy of a Subsystem
• The quantum to classical transition for random walks
• Loschmidt Echo
• Electric quantum walks with individual atoms
• Information Scrambling and Loschmidt Echo
• Quantum Chaos Border for Quantum Computing
• Testing statistical bounds on entanglement using quantum chaos
• Entangling power of quantized chaotic systems
• Dynamical aspects of quantum entanglement for weakly coupled kicked tops
• Optimizing the discrete time quantum walk using a SU(2) coin
• Entanglement production in coupled chaotic systems : Case of the Kicked Tops
• Quantum Walks in artificial electric and gravitational Fields
• Quantum chaos and random matrix theoryfor fidelity decay in quantum computationswith static imperfections
• Decoherence induced by a chaotic environment: A quantum walker with a complex coin
• Diffusive-ballistic crossover in 1D quantum walks
• Intrinsic decoherence and classical-quantum correspondence in two coupled delta-kicked rotors
• Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
• Creating cat states in one-dimensional quantum walks using delocalized initial states
• Entanglement critical length at the many-body localization transition
• Entanglement production by interaction quenches of quantum chaotic subsystems
• Quenching and generation of random states in a kicked Ising model
• Out-of-time-ordered correlators and quantum walks
• Entropy production due to coupling to a heat bath in the kicked rotor problem
• Logarithmic entanglement growth in two-dimensional disordered fermionic systems
• Quantum walk on a toral phase space
• Path integral approach to one-dimensional discrete-time quantum walk

Cited by in corpus (5)

• Instability in the quantum restart problem
• Coined quantum walks on the line: Disorder, entanglement, and localization
• A simple coin for a $2d$ entangled walk
• Complexity for one-dimensional discrete time quantum walk circuits
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous