Quantum walks: a comprehensive review

Abstract

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

Paper accepted for publication in Quantum Information Processing Journal

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Cited by in corpus (452)

• Photonic quantum information processing: a review
• Microscopic observation of magnon bound states and their dynamics
• Strongly Correlated Quantum Walks in Optical Lattices
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Quantum speedup of Monte Carlo methods
• Random Walks: A Review of Algorithms and Applications
• Quantum Computer Systems for Scientific Discovery
• Emerging quantum computing algorithms for quantum chemistry
• Electric quantum walks with individual atoms
• Nonseparable states of light: From quantum to classical
• Dynamical moments reveal a topological quantum transition in a photonic quantum walk
• A review of Quantum Cellular Automata
• Machine learning for long-distance quantum communication
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• High-dimensional frequency crystals and quantum walks in electro-optic microcombs
• Thermodynamic uncertainty relation for general open quantum systems
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
• Experimental engineering of arbitrary qudit states with discrete-time quantum walks
• Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
• Realization of single-qubit positive operator-valued measurement via a one-dimensional photonic quantum walk
• Quantum Google in a Complex Network
• Biology and medicine in the landscape of quantum advantages
• Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs
• Two-dimensional topological quantum walks in the momentum space of structured light
• Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
• Quantum walk as a generalized measuring device
• Scattering theory of topological phases in discrete-time quantum walks
• Repeated interactions in open quantum systems
• Quantum Transport Enhancement by Time-Reversal Symmetry Breaking
• Speed limits and locality in many-body quantum dynamics
• Anderson localization in generalized discrete time quantum walks
• Survival of classical and quantum particles in the presence of traps
• Electric-circuit simulation of the Schrödinger equation and non-Hermitian quantum walks
• Quantum key distribution with quantum walks
• Entangling Power of Disordered Quantum Walks
• Quantum walks of a phonon in trapped ions
• Universally Optimal Noisy Quantum Walks on Complex Networks
• Quantum state engineering using one-dimensional discrete-time quantum walks
• Staggered Quantum Walks on Graphs
• Centrality measure based on continuous-time quantum walks and experimental realization
• Weak Limit of the 3-State Quantum Walk on the Line
• Quantum walks on graphs representing the firing patterns of a quantum neural network
• A comprehensive review on developments of synthetic dimensions
• Quantum walks in external gauge fields
• Quantum Logic with Interacting Bosons in 1D
• Transport properties of continuous-time quantum walks on Sierpinski fractals
• Dynamic-Disorder-Induced Enhancement of Entanglement in Photonic Quantum Walks
• Playing a true Parrondo's game with a three state coin on a quantum walk
• Complex Quantum Networks: a Topical Review
• Limit theorems for open quantum random walks
• Non-Markovian continuous-time quantum walks on lattices with dynamical noise
• Implementing Parrondo's paradox with two coin quantum walks
• Discrete-time quantum walk with feed-forward quantum coin
• Predicting quantum advantage by quantum walk with convolutional neural networks
• Quantum percolation and transition point of a directed discrete-time quantum walk
• Large scale quantum walks by means of optical fiber cavities
• Quantum computing for chemistry and physics applications from a Monte Carlo perspective
• Ultra-long quantum walks via spin-orbit photonics
• Dirac Quantum Cellular Automaton from Split-step Quantum Walk
• Quantum walks with memory - goldfish, elephants and wise old men
• Quantum walks of two correlated photons in a 2D synthetic lattice
• Quantum walks of interacting fermions on a cycle graph
• Experimental investigation of superdiffusion via coherent disordered Quantum Walks
• A versatile quantum walk resonator with bright classical light
• Quantum transport in d-dimensional lattices
• Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons
• Quantum walks with an anisotropic coin I: spectral theory
• Controlling quantum random walk with a step-dependent coin
• Experimental demonstration of quantum walks with initial superposition states
• Driven Quantum Walks
• Quantum walks with sequential aperiodic jumps
• Spectral Stability of Unitary Network Models
• Quantum asymmetry between time and space
• Establishing the equivalence between Szegedy's and coined quantum walks using the staggered model
• Manipulating non-reciprocity in a two-dimensional magnetic quantum walk
• Quantum topology identification with deep neural networks and quantum walks
• The Open Quantum Brownian Motion
• Group transformations and entangled-state quantum gates with directionally unbiased linear-optical multiports
• Experimental realization of quantum teleportation using coined quantum walks
• Experimental realization of a momentum-space quantum walk
• Green's function approach for quantum graphs: an overview
• The Elephant Quantum Walk
• Quantum Walk in Degenerate Spin Environments
• Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers
• Staggered Quantum Walks with Hamiltonians
• Equivalence of Szegedy's and Coined Quantum Walks
• Dynamics and energy spectra of aperiodic discrete-time quantum walks
• Relational Proofs for Quantum Programs
• Discrete-time quantum walk algorithm for ranking nodes on a network
• From classical to quantum walks with stochastic resetting on networks
• Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
• Analyzing the impact of time-correlated noise on zero-noise extrapolation
• Enhanced non-Markovian behavior in quantum walks with Markovian disorder
• Noisy quantum walks of two indistinguishable interacting particles
• Optical quantum computing with photons of arbitrarily low fidelity and purity
• Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
• One-Dimensional Coinless Quantum Walks
• Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
• Incoherent non-Hermitian skin effect in photonic quantum walks
• Quantum random access memory via quantum walk
• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Measurement induced quantum walks on an IBM Quantum Computer
• Persistence of Topological Phases in Non-Hermitian Quantum Walks
• Quantum spatial search in two-dimensional waveguide arrays
• Creating cat states in one-dimensional quantum walks using delocalized initial states
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• Benchmarking projective simulation in navigation problems
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• Quantized recurrence time in iterated open quantum dynamics
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• Localization in Quantum Walks on a Honeycomb Network
• Machine learning transfer efficiencies for noisy quantum walks
• Dynamics of Rydberg excitations and quantum correlations in an atomic array coupled to a photonic crystal waveguide
• Subdiffusion via Disordered Quantum Walks
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• Link prediction with continuous-time classical and quantum walks
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• Analysis of Coined Quantum Walks with Renormalization
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• Quantum walks on embedded hypercubes
• Time evolution of continuous-time quantum walks on dynamical percolation graphs
• Quantum algorithms for scientific computing
• Feedback-assisted quantum search by continuous-time quantum walks
• Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions
• Quantum walk transport on carbon nanotube structures
• Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
• Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
• Generation of hyperentangled states and two-dimensional quantum walks using $J$- ($q$)- plates and polarization beamsplitters
• Continuous-time quantum walks on planar lattices and the role of the magnetic field
• Quantum walks with memory on cycles
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• Quantum correlations of identical particles subject to classical environmental noise
• Steady states of continuous-time open quantum walks
• Quantum magnetometry using discrete-time quantum walk
• Efficient implementation of discrete-time quantum walks on quantum computers
• Deterministic spatial search using alternating quantum walks
• Classical Artificial Neural Network Training Using Quantum Walks as a Search Procedure
• Detection of edge defects by embedded eigenvalues of quantum walks
• One dimensional lazy quantum walks and occupancy rate
• Entropy rate of message sources driven by quantum walks
• Strongly trapped two-dimensional quantum walks
• Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks
• Interacting quantum walkers: Two-body bosonic and fermionic bound states
• Exceptional Quantum Walk Search on the Cycle
• On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
• Implementation of a 3 x 3 directionally-unbiased linear optical multiport
• Accelerated quantum walk, two-particle entanglement generation and localization
• Quantum walk on a cylinder
• Percolated quantum walks with a general shift operator: From trapping to transport
• Trojan Quantum Walks
• Machine learning classification of non-Markovian noise disturbing quantum dynamics
• Discrete time quantum walk with nitrogen-vacancy centers in diamond coupled to a superconducting flux qubit
• Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states
• Entanglement and interaction in a topological quantum walk
• A counterintuitive role of geometry in transport by quantum walks
• One-Dimensional Lazy Quantum walk in Ternary System
• Edge states in a two-dimensional quantum walk with disorder
• Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
• Quantum simulation of topologically protected states using directionally unbiased linear-optical multiports
• Quantum Financial Modeling on Noisy Intermediate-Scale Quantum Hardware: Random Walks using Approximate Quantum Counting
• Probing the sign of on-site Hubbard interaction by two-particle quantum walks
• Exploring LLM-Driven Explanations for Quantum Algorithms
• Efficient parallelization of quantum basis state shift
• Bosonic Quantum Error Correction with Neutral Atoms in Optical Dipole Traps
• Full Characterization of Oscillatory Localization of Quantum Walks
• Driven Discrete Time Quantum Walks
• Localization and Recurrence of Quantum Walk in Periodic Potential on a Line
• Quantum search with interacting Bose-Einstein condensates
• One-Dimensional Quantum Walks with a Position-Dependent Coin
• Quantum Walk on the Line through Potential Barriers
• Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits
• Conditional Probability Distributions of Finite Absorbing Quantum Walks
• General condition of quantum teleportation by one-dimensional quantum walks
• Scattering and perturbation theory for discrete-time dynamics
• Multi-qubit quantum computing using discrete-time quantum walks on closed graphs
• Correlations in few two-component quantum walkers on a tilted lattice
• Understanding and controlling N-dimensional quantum walks via dispersion relations. Application to the 2D and 3D Grover walks: Diabolical points and more
• Invariance in quantum walks with time-dependent coin operators
• Parrondo's effect in continuous-time quantum walks
• To Measure, or Not to Measure, That is the Question
• Lively quantum walks on cycles
• Some limit laws for quantum walks with applications to a version of the Parrondo paradox
• The Lackadaisical Quantum Walker is NOT Lazy at all
• Quantum ratchet in disordered quantum walk
• Circuit Implementation of Discrete-Time Quantum Walks via the Shunt Decomposition Method
• Coined Quantum Walks as Quantum Markov Chains
• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Probability distributions for Markov chains based quantum walks
• The uniform measure for quantum walk on hypercube: a quantum Bernoulli noises approach
• Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks
• Quantum walker as a probe for its coin parameter
• Quantum percolation in quasicrystals using continuous-time quantum walk
• Quantum walk on the Bloch sphere
• A robust approach for time-bin encoded photonic quantum information protocols
• Swift chiral quantum walks
• Discrete dynamics and non-Markovianity
• Unveiling and exemplifying the unitary equivalence of discrete time quantum walk models
• Optimizing the spatial spread of a quantum walk
• Unusual scaling in a discrete quantum walk with random long range steps
• A novel approach for quantum financial simulation and quantum state preparation
• Localization of discrete time quantum walks on the glued trees
• Continuous-Time Quantum Walks on Directed Bipartite Graphs
• Disorder-induced two-body localised state in interacting quantum walks
• Two component quantum walk in one-dimensional lattice with hopping imbalance
• Quantum-walk search in motion
• Complete classification of trapping coins for quantum walks on the 2D square lattice
• Lazy Open Quantum Walks
• Duality in Quantum Quenches and Classical Approximation Algorithms: Pretty Good or Very Bad
• Dynamic conditioning of two particle discrete-time quantum walks
• Non-classical measurement statistics induced by a coherent spin environment
• The quantum theory of time, the block universe and human experience
• Long-lived quantum speedup based on plasmonic hot spot systems
• Controlled quantum search on structured databases
• Quantum Information Approach to Dynamical Diffraction Theory
• A spectral analysis of discrete-time quantum walks related to the birth and death chains
• Spatial search by continuous-time quantum walks on renormalized Internet networks
• Cycle discrete-time quantum walks on a noisy quantum computer
• Running Measurement Protocol for the Quantum First-detection problem
• The graph tessellation cover number: extremal bounds, efficient algorithms and hardness
• The tessellation problem of quantum walks
• Robust quantum state engineering through coherent localization in biased-coin quantum walks
• Quantum Walks on Sierpinski Gaskets
• Uncertainty relation between detection probability and energy fluctuations
• Twisted quantum walks, generalised Dirac equation and Fermion doubling
• Nonlinear flip-flop quantum walks through potential barriers
• Quantum State Discrimination on Reconfigurable Noise-Robust Quantum Networks
• Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics
• Unification of energy concepts in generalised phase space theories
• The walker speaks its graph: global and nearly-local probing of the tunnelling amplitude in continuous-time quantum walks
• Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk
• Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's Theorem
• Complexity Bounds on Quantum Search Algorithms in finite-dimensional Networks
• Chirality from quantum walks without quantum coin
• Driven Gaussian quantum walks
• Feynman checkers: towards algorithmic quantum theory
• Quantum walk with a general coin: Exact solution and asymptotic properties
• Principles underlying efficient exciton transport unveiled by information-geometric analysis
• Parrondo's paradox in quantum walks with inhomogeneous coins
• Topological transition of a non-Markovian dissipative quantum walk
• Flux induced re-entrant dynamics in the quantum walk of interacting bosons
• Grover Walks on a Line with Absorbing Boundaries
• Quantum walks in polycyclic aromatic hydrocarbons
• Quantum walk of two anyons across a statistical boundary
• Enhancing nonclassical bosonic correlations in a Quantum Walk network through experimental control of disorder
• Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators
• Quantum hub and authority centrality measures for directed networks based on continuous-time quantum walks
• Eigenvalues of two-state quantum walks induced by the Hadamard walk
• Role of symmetry in quantum search via continuous-time quantum walk
• Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics
• Null-eigenvalue localization of quantum walks on real-world complex networks
• Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning
• Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
• Topological metals constructed by sliding quantum wire arrays
• Spectral Properties of Quantum Walks on Rooted Binary Trees
• Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins
• From reasonable postulates to generalised Hamiltonian systems
• Doubling the Success of Quantum Walk Search Using Internal-State Measurements
• From quantum-enhanced to quantum-inspired Monte Carlo
• Topological classification of time-asymmetry in unitary quantum processes
• Discrete-time quantum walk dispersion control through long-range correlations
• Quantum smoothed particle hydrodynamics algorithm inspired by quantum walks
• Quantum Algorithm for Smoothed Particle Hydrodynamics
• History Dependent Quantum Walk on the Cycle with an Unbalanced Coin
• One-dimensional quantum walks driven by two-entangled-qubit coins
• Coined quantum walks on the line: Disorder, entanglement, and localization
• Thermalization of Fermionic Quantum Walkers
• Quantum information spreading in a disordered quantum walk
• Quantum walk on a chimera graph
• Absence of wave operators for one-dimensional quantum walks
• Experimental Simulation of Bosonic Creation and Annihilation Operators in a Quantum Processor
• An algorithm to factorize quantum walks into shift and coin operations
• Quantum Path Computing: Computing Architecture with Propagation Paths in Multiple Plane Diffraction of Classical Sources of Fermion and Boson Particles
• Lackadaisical quantum walk in the hypercube to search for multiple marked vertices
• Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study
• Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks
• Quantum Corralling
• Open system approach to Neutrino oscillations in a quantum walk framework
• Quantum walks on two kinds of two-dimensional models
• Light-cone and local front dynamics of a single-particle extended quantum walk
• A framework for optimal quantum spatial search using alternating phase-walks
• On Fermionic walkers interacting with a correlated structured environment
• Unifying quantum spatial search, state transfer and uniform sampling on graphs: simple and exact
• The switching effect of the side chain on quantum walks on triple graphs
• Mean hitting times of quantum Markov chains in terms of generalized inverses
• Short time behavior of continuous time quantum walks on graphs
• From Classical to quantum stochastic process
• Non-markovianity and bound states in quantum walks with a phase impurity
• Gossip Algorithms in Quantum Networks
• Fermionic walkers driven out of equilibrium
• On the equivalence between quantum and random walks on finite graphs
• Quantum walk processes in quantum devices
• Accelerated first detection in discrete-time quantum walks using sharp restarts
• Dynamical Phase Transitions in Open Quantum Walks
• New theory of diffusive and coherent nature of optical wave via a quantum walk
• Borromean states in discrete-time quantum walks
• Spectral Properties of Non-Unitary Band Matrices
• Phase transition of an open quantum walk
• Superdiffusivity of quantum walks: A Feynman sum-over-paths description
• QReach: A Reachability Analysis Tool for Quantum Markov Chains
• A limit law of the return probability for a quantum walk on a hexagonal lattice
• Photonic random walks with traps
• Finite-element assembly approach of optical quantum walk networks
• High-fidelity state transfer via quantum walks from delocalized states
• Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk
• Weak limits for quantum walks on the half-line
• Quantum Walk on Orbit Spaces
• Anderson localization without eigenstates in photonic quantum walks
• Scattering Expansion for Localization in One Dimension: from Disordered Wires to Quantum Walks
• History states of one-dimensional quantum walks
• Anomalous transport in periodic photonic chains with designed loss
• Optical realization of one-dimensional generalized split-step quantum walks
• Experimental quantum state transfer of an arbitrary single-qubit state on a cycle with four vertices using a coined quantum random walk
• Universal dynamical scaling laws in three-state quantum walks
• Exponential speedups for quantum walks in random hierarchical graphs
• Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
• Nonclassical oscillations in pre- and post-selected quantum walks
• Feynman checkers: the probability to find an electron vanishes nowhere inside the light cone
• Quantum Stochastic Walk Models for Quantum State Discrimination
• On the potential of quantum walks for modeling financial return distributions
• Quantum walks and entanglement in cavity networks
• Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs
• Hitting time for quantum walks of identical particles
• Two-particle coined-quantum walk with long-range interaction
• Nonstabilizerness generation in a multiparticle quantum walk
• Analytical expression for variance of homogeneous-position quantum walk with decoherent position
• Hitting statistics from quantum jumps
• Spin-1 Quantum Walks
• Quantum centipedes: collective dynamics of interacting quantum walkers
• Dequantization via quantum channels
• Escaping Local Minima with Quantum Coherent Cooling
• Analytical solutions for quantum walks on 1D chain with different shift operators
• Influence of coin symmetry on infinite hitting times in quantum walks
• Dynamics and computation in linear open quantum walks
• Strong analog classical simulation of coherent quantum dynamics
• Directivity of quantum walk via its random walk replica
• Disorder-free localisation in continuous-time quantum walks : Role of symmetries
• Transport and Localization in Quantum Walks on a Random Hierarchy of Barriers
• Quantum walk for SU(1,1)
• The syntactic side of autonomous categories enriched over generalised metric spaces
• Wigner formalism for a particle on an infinite lattice: dynamics and spin
• On Hitting Times for General Quantum Markov Processes
• Scattering Expansion for Localization in One Dimension
• Quantum walks as thermalizations, with application to fullerene graphs
• Lower Bounds on the Localisation Length of Balanced Random Quantum Walks
• Effective simulation of state distribution in qubit chains
• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
• Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles
• Quantum vs Classical Birth and Death Processes; Exactly Solvable Examples
• One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
• Quantum Ultra-Walks: Walks on a Line with Hierarchical Spatial Heterogeneity
• Optimal quantum transport on a ring via locally monitored chiral quantum walks
• Quantum transfer through small networks coupled to phonons: effects of topology vs phonons
• Deterministic generation of hybrid entangled states using quantum walks
• Programmable non-Hermitian photonic quantum walks via dichroic metasurfaces
• Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit-qudit dynamics
• A quantum walk on the half line with a particular initial state
• Optimization for the propagation of a multiparticle quantum walk in a one-dimensional lattice
• Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian
• Perfect state transfer using Markovian quantum walk
• Experimental measurement of quantum first-passage-time distributions
• Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling
• Deutsch-Jozsa and Bernstein-Vazirani algorithm using single-particle discrete-time quantum walk
• Bidirectional quantum teleportation using quantum walks
• Bosonic Entanglement and Quantum Sensing from Energy Transfer in two-tone Floquet Systems
• Two-dimensional quantum central limit theorem by quantum walks
• Quantum walk with coherent multiple translations induces fast quantum gate operations
• Compact and programmable large-scale optical processor in free space
• Dissipative realization of a quantum distance-based classifier using open quantum walks
• Quantum Hitting Time according to a given distribution
• Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks
• Repeated measurements and random scattering in quantum walks
• Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Directional quantum random walk induced by coherence
• Invariance in Quantum Walks
• Spectral Property of Magnetic Quantum Walk on Hypercube
• Dynamical Localization and Transport properties of Quantum Walks on the hexagonal lattice
• The role of coherence on two-particle quantum walks
• Hypercube Quantum Search: Exact Computation of the Probability of Success in Polynomial Time
• Quantum Magic in Discrete-Time Quantum Walk
• Simulating the discrete-time quantum walk dynamics with simultaneous coin and shift operators
• Decoherence and classicalization of continuous-time quantum walks on graphs
• Mimicking the Hadamard discrete-time quantum walk with a time-independent Hamiltonian
• Realizing non-trivial doublon formation using a quantum computer
• Complementarity in quantum walks
• Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
• Quantum walks assisted by particle number fluctuations
• Influence of generic quantum coins on the spreading and entanglement in binary aperiodic quantum walks
• A limit theorem for a splitting distribution of a quantum walk
• The localization of quantum random walks on sierpinski gaskets
• Conserved Quantities in Linear and Nonlinear Quantum Search
• Quantum walk mixing is faster than classical on periodic lattices
• Quantum spatial best-arm identification via quantum walks
• Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
• Absorption-based qubit estimation in discrete-time quantum walks
• Crystalline Spectral Form Factors
• Quantum state transfer and periodicity in discrete-time quantum walks under non--Markovian dephasing noise
• Temporal nonclassicality in continuous-time quantum walks
• Correlated dynamics of three-particle bound states induced by emergent impurities in Bose-Hubbard model
• A simple model of quantum walk with a gap in distribution
• Transition in Splitting Probabilities of Quantum Walks
• Quantum states supported by matroids
• Many-Body Effects in a Molecular Quantum NAND Tree
• Hybrid atom-molecule quantum walks in one-dimensional optical lattice
• Efficient Scheme of Experimental Quantifying non-Markovianity in High-Dimension Systems
• Robustness and classical proxy of entanglement in variants of quantum walk
• Feynman checkers: through the looking-glass
• Phase transition of a continuous-time quantum walk on the half line
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Return probability of quantum and correlated random walks
• Quantum walks advantage on the dihedral group for uniform sampling problem
• Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle problem
• Limit distribution of a time-dependent quantum walk on the half line
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• Search Via quantum walks with intermediate measurements
• Quantum Coin Flipping, Qubit Measurement and Generalized Fibonacci Numbers
• Faster Search of Clustered Marked States with Lackadaisical Quantum Walks
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous
• Topology identification of autonomous quantum dynamical networks
• Response to glassy disorder in coin on spread of quantum walker
• Complexity for one-dimensional discrete time quantum walk circuits
• Key graph properties affecting transport efficiency of flip-flop Grover percolated quantum walks
• Quantum walks under superposition of causal order
• Feynman checkers: lattice quantum field theory with real time
• Skeleton structure inherent in discrete-time quantum walks
• Optimal detection of quantum states via projective measurements