Quantum random walks - an introductory overview

Abstract

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions.

20 pages, 13 figures, to appear in Contemporary Physics

Cited by in corpus (726)

• Quantum walks of correlated particles
• Quantum walks: a comprehensive review
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• The quest for a Quantum Neural Network
• Random walks and diffusion on networks
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Vibrations, Quanta and Biology
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Realization of a quantum walk with one and two trapped ions
• Quantum transport simulations in a programmable nanophotonic processor
• Universal quantum computation using the discrete time quantum walk
• Anderson localization of entangled photons in an integrated quantum walk
• Discrete single-photon quantum walks with tunable decoherence
• Simulating chemistry using quantum computers
• Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
• Random Walks: A Review of Algorithms and Applications
• Spin-Based Quantum Computers made by Chemistry: Hows and Whys
• What is the Computational Value of Finite Range Tunneling?
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Decoherence in quantum walks - a review
• Weak limits for quantum random walks
• Quantum walks and wavepacket dynamics on a lattice with twisted photons
• Photonic quantum walk in a single beam with twisted light
• Quantum Computing with NMR
• Emerging quantum computing algorithms for quantum chemistry
• Quantum Correlations in Two-Particle Anderson Localization
• Quantum Simulations of Classical Annealing Processes
• Quantum walk on the line as an interference phenomenon
• Quantum photonics at telecom wavelengths based on lithium niobate waveguides
• Photon propagation in a discrete fiber network: An interplay of coherence and losses
• Open Quantum Random Walks
• Localization of Two-Dimensional Quantum Walks
• Entanglement in coined quantum walks on regular graphs
• Quantum Walk on a Line with Two Entangled Particles
• Two-photon quantum walks in an elliptical direct-write waveguide array
• Hitting time for quantum walks on the hypercube
• Quantum Algorithm Implementations for Beginners
• Quantum speed-up in collisional battery charging
• Decoherence in the quantum walk on the line
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Aperiodic Quantum Random Walks
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Quantum Walks on a Random Environment
• Asymptotic evolution of quantum walks with random coin
• Quantum stochastic walks: A generalization of classical random walks and quantum walks
• Optimizing the discrete time quantum walk using a SU(2) coin
• Localization and its consequences for quantum walk algorithms and quantum communication
• Quantum walk on the line: entanglement and non-local initial conditions
• Topological phases and delocalization of quantum walks in random environments
• Machine learning for long-distance quantum communication
• A quantum version of Wielandt's inequality
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• Relativistic quantum walks
• Optical mesh lattices with PT-symmetry
• Implementing Quantum Walks Using Orbital Angular Momentum of Classical Light
• Quantum Navigation and Ranking in Complex Networks
• Survival Probabilities in Coherent Exciton Transfer with Trapping
• Classical approach to the graph isomorphism problem using quantum walks
• Quantum query complexity of some graph problems
• Experimental engineering of arbitrary qudit states with discrete-time quantum walks
• Experimental quantum-walk revival with a time-dependent coin
• Fast Escape from Quantum Mazes in Integrated Photonics
• Quantum Walk of Two Interacting Bosons
• Efficient Quantum Walk on a Quantum Processor
• Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
• Limit distributions of two-dimensional quantum walks
• Realization of single-qubit positive operator-valued measurement via a one-dimensional photonic quantum walk
• Quantum Machine Learning: from physics to software engineering
• Quantum Networks on Cubelike Graphs
• Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
• Quantum walk on a line for a trapped ion
• Quantum walks with encrypted data
• Grover Search with Lackadaisical Quantum Walks
• Quantum walks with infinite hitting times
• Simulation of quantum random walks using interference of classical field
• Quantum walk approach to search on fractal structures
• Perfect state transfer in cubelike graphs
• Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs
• Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
• Quantum random walk of two photons in separable and entangled state
• Trapping a particle of a quantum walk on the line
• Quantum speedup of classical mixing processes
• Error tolerance of the BosonSampling model for linear optics quantum computing
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Disordered Quantum Walks in one lattice dimension
• Perfect state transfer and efficient quantum routing: a discrete-time quantum walk approach
• Quantum walk-based search and centrality
• Multi-walker discrete time quantum walks on arbitrary graphs, their properties, and their photonic implementation
• Quantum walks on quotient graphs
• Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
• A synthetic gauge field for two-dimensional time-multiplexed quantum random walks
• Quantum Walk with a time-dependent coin
• Optimal state encoding for quantum walks and quantum communication over spin systems
• Experimental realisation of a delayed-choice quantum walk
• Localization of Multi-State Quantum Walk in One Dimension
• Quantum searches on highly symmetric graphs
• Quantum walk as a generalized measuring device
• Counting Statistics of Many-Particle Quantum Walks
• One- and two-dimensional quantum walks in arrays of optical traps
• Quantum random walk on the line as a markovian process
• Optical Cavity Implementations of the Quantum Walk
• The Dirac equation as a quantum walk: higher dimensions, observational convergence
• Quantum walks with random phase shifts
• Coherent Ising machines -- Quantum optics and neural network perspectives
• Bringing order through disorder: Localization of errors in topological quantum memories
• Quantum Random Walks do not need a Coin Toss
• Restart expedites quantum walk hitting times
• Non-Markovian evolution: a quantum walk perspective
• Spacetime structures of continuous time quantum walks
• Quantum transport and localization in 1d and 2d tight-binding lattices
• Symmetries and noise in quantum walk
• Decoherence vs entanglement in coined quantum walks
• A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime
• Repeated interactions in open quantum systems
• Quantum walks on cycles
• Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk
• Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
• Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices
• Quantum Transport Enhancement by Time-Reversal Symmetry Breaking
• Quantum random walks with history dependence
• Nonlinear optical Galton board
• Harnessing symmetry to control quantum transport
• Anderson localization in generalized discrete time quantum walks
• Hitting time for the continuous quantum walk
• Universal quantum computation by discontinuous quantum walk
• Free Dirac evolution as a quantum random walk
• Weak-value amplification as an optimal metrological protocol
• Quantum phase transition using quantum walks in an optical lattice
• Alternate two-dimensional quantum walk with a single-qubit coin
• Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions
• Almost uniform sampling via 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
• Asymptotic dynamics of coined quantum walks on percolation graphs
• Quantum key distribution with quantum walks
• Entangling Power of Disordered Quantum Walks
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Consensus for Quantum Networks: From Symmetry to Gossip Iterations
• Universally Optimal Noisy Quantum Walks on Complex Networks
• Quantum Walks, Quantum Gates and Quantum Computers
• Decoherence in one-dimensional Quantum Walk
• Quantum state engineering using one-dimensional discrete-time quantum walks
• Phase-space approach to the study of decoherence in quantum walks
• Quantum walk approach to simulating parton showers
• Centrality measure based on continuous-time quantum walks and experimental realization
• Review on Quantum Walk Computing: Theory, Implementation, and Application
• Two quantum walkers sharing coins
• Weak Limit of the 3-State Quantum Walk on the Line
• Quantum walks on graphs representing the firing patterns of a quantum neural network
• Modifying quantum walks: A scattering theory approach
• Scattering theory and discrete-time quantum walks
• Control by quantum dynamics on graphs
• Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications
• Combinatorial optimisation via highly efficient quantum walks
• Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits
• Asymptotic behavior of quantum walks on the line
• Slow transport by continuous time quantum walks
• Mixing Times in Quantum Walks on the Hypercube
• Dynamics of continuous-time quantum walks in restricted geometries
• Degree Distribution in Quantum Walks on Complex Networks
• Asymptotic entanglement in a two-dimensional quantum walk
• Quantum Logic with Interacting Bosons in 1D
• Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
• Distribution of chirality in the quantum walk: Markov process and entanglement
• Decoherence induced by a chaotic environment: A quantum walker with a complex coin
• On the optimality of spatial search by continuous-time quantum walk
• Limit theorems for open quantum random walks
• Complex Quantum Networks: a Topical Review
• Quantum simulation of electron-phonon interactions in strongly deformable materials
• Non-Markovian continuous-time quantum walks on lattices with dynamical noise
• Perfect quantum state transfer with spinor bosons on weighted graphs
• Machine learning \& artificial intelligence in the quantum domain
• Quantum Walks with Dynamical Control: Graph Engineering, Initial State Preparation and State Transfer
• Wigner formula of rotation matrices and quantum walks
• Discrete-time quantum walk with feed-forward quantum coin
• Driving quantum walk spreading with the coin operator
• Coherent transport on Apollonian networks and continuous-time quantum walks
• Predicting quantum advantage by quantum walk with convolutional neural networks
• Large scale quantum walks by means of optical fiber cavities
• A quantum random walk of a Bose-Einstein condensate in momentum space
• Universal quantum computing using single-particle discrete-time quantum walk
• Quantum search algorithms on a regular lattice
• The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials
• Quantum simulation of bosonic-fermionic non-interacting particles in disordered systems via quantum walk
• Random Time-Dependent Quantum Walks
• Quantum walks public key cryptographic system
• Propagating Quantum Walks: the origin of interference structures
• Quantum walks with memory - goldfish, elephants and wise old men
• Asymmetries in symmetric quantum walks on two-dimensional networks
• Experimental investigation of superdiffusion via coherent disordered Quantum Walks
• Directional correlations in quantum walks with two particles
• Quantum Computing for Fusion Energy Science Applications
• Ultrafast dynamics of photoinduced charge separation
• Searching via walking: How to find a marked subgraph of a graph using quantum walks
• Generalized Quantum Walk in Momentum Space
• Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
• Decoherence and Quantum Walks: anomalous diffusion and ballistic tails
• Search on a Hypercubic Lattice using a Quantum Random Walk: I. d>2
• Models of quantum computation and quantum programming languages
• Quantum search on graphene lattices
• Localisation, delocalisation, and topological transitions in disordered 2D quantum walks
• Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons
• Quantum Martingale Theory and Entropy Production
• Perfect wave-packet splitting and reconstruction in a one-dimensional lattice
• Coherent Time Evolution and Boundary Conditions of Two-Photon Quantum Walks
• Driven Quantum Walks
• Discrete Spacetime and Relativistic Quantum Particles
• Experimental demonstration of quantum walks with initial superposition states
• Effects of long-range hopping and interactions on quantum walk in ordered and disordered lattices
• Quantum walks with sequential aperiodic jumps
• Controlling quantum random walk with a step-dependent coin
• Spectral Stability of Unitary Network Models
• Trapping photons on the line: controllable dynamics of a quantum walk
• Faster transport with a directed quantum walk
• Continuous-time quantum walks on one-dimension regular networks
• Quantum walk coherences on a dynamical percolation graph
• A quantum-walk-inspired adiabatic algorithm for graph isomorphism
• Continuous-time quantum walks on star graphs
• Experimental simulation and limitations of quantum walks with trapped ions
• Group transformations and entangled-state quantum gates with directionally unbiased linear-optical multiports
• Spatial Search by Continuous-Time Quantum Walk with Multiple Marked Vertices
• The Open Quantum Brownian Motion
• Survival probability in a one-dimensional quantum walk on a trapped lattice
• Spatial entanglement using a quantum walk on a many-body system
• Emergence of Randomness and Arrow of Time in Quantum Walks
• Free Fermions with a Localized Source
• Qubit state transfer via discrete-time quantum walks
• Relativistic effects in quantum walks: Klein's paradox and Zitterbewegung
• Experimental realization of a momentum-space quantum walk
• Search on a Fractal Lattice using a Quantum Random Walk
• A Quantum Graph Approach to Metamaterial Design
• Quantum Search with Multiple Walk Steps per Oracle Query
• Green's function approach for quantum graphs: an overview
• High-fidelity state transfer through long-range correlated disordered quantum channels
• Equivalence of Szegedy's and Coined Quantum Walks
• Localized State in a Two-Dimensional Quantum Walk on a Disordered Lattice
• Relational Proofs for Quantum Programs
• Quantum butterfly effect in polarized Floquet systems
• Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers
• Discrete-time quantum walk algorithm for ranking nodes on a network
• Implementation of multidimensional quantum walks using linear optics and classical light
• Dynamics and energy spectra of aperiodic discrete-time quantum walks
• Open Quantum Walks: a short introduction
• The Fibonacci quantum walk and its cassical trace map
• Fast Black-Box Quantum State Preparation
• Quantum walks and orbital states of a Weyl particle
• Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs
• Quantum state revivals in quantum walks on cycles
• Experimental parity-time symmetry quantum walks on a directed graph
• Noisy quantum walks of two indistinguishable interacting particles
• Quantum random walks using quantum accelerator modes
• Implementation of a spatial two-dimensional quantum random walk with tunable decoherence
• Enhanced non-Markovian behavior in quantum walks with Markovian disorder
• Quantum search algorithms on the hypercube
• Optical quantum computing with photons of arbitrarily low fidelity and purity
• Non-Unitary Quantum Walks on Hyper-Cycles
• Quantum Walk with a four-dimensional coin
• Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
• Collider Events on a Quantum Computer
• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Quantum dynamics on a lossy non-Hermitian lattice
• Approximating the quantum approximate optimization algorithm with digital-analog interactions
• Quantum walks in synthetic gauge fields with 3D integrated photonics
• Equivalence between discrete quantum walk models in arbitrary topologies
• Continuous-Time Quantum Walks and Trapping
• Open quantum random walks: bi-stability on pure states and ballistically induced diffusion
• When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?
• Scattering quantum random-walk search with errors
• Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk
• Persistence of Topological Phases in Non-Hermitian Quantum Walks
• Quantum spatial search in two-dimensional waveguide arrays
• Quantum Walks, Weyl equation and the Lorentz group
• The Limiting Distribution of Decoherent Quantum Random Walks
• Sub-ballistic behavior in quantum systems with Lévy noise
• The meeting problem in the quantum random walk
• Creating cat states in one-dimensional quantum walks using delocalized initial states
• Optical implementability of the two-dimensional Quantum Walk
• Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems
• Continuous time quantum walks in phase space
• Quantum transport on two-dimensional regular graphs
• Entanglement dynamics and quasi-periodicity in discrete quantum walks
• A Comparison of Quantum Walk Implementations on NISQ Computers
• Scattering model for quantum random walk on the hypercube
• Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
• Search on a Hypercubic Lattice through a Quantum Random Walk: II. d=2
• Photonic Discrete-time Quantum Walks and Applications
• Asymptotic entanglement in quantum walks from delocalized initial states
• QSWalk: a Mathematica package for quantum stochastic walks on arbitrary graphs
• Electric quantum walks in two dimensions
• Quantum walks: decoherence and coin-flipping games
• Quantum walk on circles in phase space
• Quantum walk of a Bose-Einstein condensate in the Brillouin zone
• Spin systems dynamics and faults detection in threshold networks
• Decoherent quantum walks driven by a generic coin operation
• Mixing Times in Quantum Walks on Two-Dimensional Grids
• Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk
• Quantum walks in commensurate off-diagonal Aubry-André-Harper model
• Continuous-Time Quantum Walks on Dynamic Graphs
• Faster Quantum Walk Search on a Weighted Graph
• Extraordinary behaviors in two-dimensional decoherent alternative quantum walk
• Bose-Hubbard model for universal quantum walk-based computation
• Quantum and random walks as universal generators of probability distributions
• Coherent exciton transport and trapping on long-range interacting cycles
• Fermion confinement via Quantum Walks in 2D+1 and 3D+1 spacetime
• Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
• Entanglement formation in continuous-variable random quantum networks
• Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks
• Simple implementation of high fidelity controlled-$i$SWAP gates and quantum circuit exponentiation of non-Hermitian gates
• Quantum walks in weak electric fields and Bloch oscillations
• Asymptotic evolution of quantum walks on the $N$-cycle subject to decoherence on both the coin and position degrees of freedom
• Discrete spacetime, quantum walks and relativistic wave equations
• Topological quantum walks: theory and experiments
• Efficient quantum circuits for continuous-time quantum walks on composite graphs
• Experimental demonstration of a directionally-unbiased linear-optical multiport
• Quantum-Clustered Two-Photon Walks
• Faster quantum mixing for slowly evolving sequences of Markov chains
• Quantum cellular automata and quantum field theory in two spatial dimensions
• Investigation of continuous-time quantum walk on root lattice $A_n$ and honeycomb lattice
• From quantum graphs to quantum random walks
• Quantum random walks on the $N$-cycle subject to decoherence on the coin degree of freedom
• Microscopic derivation of Open Quantum Walks
• Decoherence in Two-Dimensional Quantum Random Walks with Traps
• Spectral Transition for Random Quantum Walks on Trees
• Machine learning transfer efficiencies for noisy quantum walks
• Unidirectional quantum walks: evolution and exit times
• Quantum walks on complex networks with connection instabilities and community structure
• Regular quantum graphs
• Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs
• Quantum return probability of a system of $N$ non-interacting lattice fermions
• Subdiffusion via Disordered Quantum Walks
• Steering random walks with kicked ultracold atoms
• Universal Behavior of Quantum Walks with Long-Range Steps
• Two-walker discrete-time quantum walks on the line with percolation
• Discrete time quantum walks on percolation graphs
• Link prediction with continuous-time classical and quantum walks
• Quantum walks on embedded hypercubes
• Analysis of Coined Quantum Walks with Renormalization
• Disorder-free localization in quantum walks
• Weak disorder enhancing the production of entanglement in quantum walks
• Conditional Quantum Walk and Iterated Quantum Games
• Connecting velocity and entanglement in quantum walks
• Quantum-classical distance as a tool to design optimal chiral quantum walk
• Continuous Limit of Discrete Quantum Walks
• Quantum random walk and tight-binding model subject to projective measurements at random times
• Maximal entanglement from quantum random walks
• N-dimensional alternate coined quantum walks from a dispersion relation perspective
• Simulation of Quantum Walks and Fast Mixing with Classical Processes
• Generalized open quantum walks on Apollonian networks
• Feedback-assisted quantum search by continuous-time quantum walks
• Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
• Quantum random walks without walking
• Multi-parameter quantum metrology with discrete-time quantum walks
• Decoherence in quantum walks and quantum computers
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Unitary Equivalence of Quantum Walks
• Properties of Open Quantum Walks on $\mathbb{Z}$
• Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions
• Coherent chemical kinetics as quantum walks I: Reaction operators for radical pairs
• Quantum direct communication protocols using discrete-time quantum walk
• Continuous-time quantum walks on planar lattices and the role of the magnetic field
• Simple quantum graphs proposal for quantum devices
• Entanglement measurement with discrete multiple coin quantum walks
• Control of Quantum Dynamics of Electron Transfer in Molecular Loop Structures: Spontaneous Breaking of Chiral Symmetry under Strong Decoherence
• Quantum correlations of identical particles subject to classical environmental noise
• Quantum Walk Search with Time-Reversal Symmetry Breaking
• Isotropic quantum walks on lattices and the Weyl equation
• Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
• Discrete-time quantum walks on one-dimensional lattices
• An Effective Hamiltonian Approach to Quantum Random Walk
• Quantum walks on a circle with optomechanical systems
• Entropy rate of message sources driven by quantum walks
• Signatures of non-trivial pairing in the quantum walk of two-component bosons
• Detection of discrete spacetime by matter interferometry
• Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin
• Quantum Walk with Jumps
• On limiting distributions of quantum Markov chains
• Implementation of a 3 x 3 directionally-unbiased linear optical multiport
• Quantum Persistence: A Random Walk Scenario
• Quantum Cloning by Cellular Automata
• Quantum walk on a cylinder
• Continuous-Time Quantum Random Walks Require Discrete Space
• Interacting quantum walkers: Two-body bosonic and fermionic bound states
• Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks
• Quantum Walks and Reversible Cellular Automata
• Birth and death processes and quantum spin chains
• Stationary States in Quantum Walk Search
• Exact results in Floquet coin toss for driven integrable models
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• A quantum dynamical approach to matrix Khrushchev's formulas
• Accelerated quantum walk, two-particle entanglement generation and localization
• Quantum Walk Search on Kronecker Graphs
• Reexamination of decoherence in quantum walks on the hypercube
• Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator
• Strongly trapped two-dimensional quantum walks
• Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{P}\mathcal{T}$ symmetric non-Hermitian system by using non-unitary quantum walks
• Bloch oscillations in the magnetoconductance of twisted bilayer graphene
• Enhanced-sensitivity interferometry with phase-sensitive unbiased multiports
• On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
• Concentric Network Symmetry
• Quantum Game Jam -- Making Games with Quantum Physicists
• Quantum tight-binding chains with dissipative coupling
• Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions
• Non-Markovian Decoherent Quantum Walks
• Machine learning classification of non-Markovian noise disturbing quantum dynamics
• Qcompiler: quantum compilation with CSD method
• Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
• Scaling and crossover behaviour in a truncated long range quantum walk
• Effects of non-local initial conditions in the Quantum Walk on the line
• Quantum walks on random lattices: Diffusion, localization and the absence of parametric quantum speed-up
• Discrete time quantum walk with nitrogen-vacancy centers in diamond coupled to a superconducting flux qubit
• Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
• Finite-size scaling analysis of binary stochastic processes and universality classes of information cascade phase transition
• Framework for discrete-time quantum walks and a symmetric walk on a binary tree
• Trojan Quantum Walks
• Experimental Control of the Degree of Non-Classicality via Quantum Coherence
• Highly noise resistant multipartite quantum correlations
• Quantum tunneling on graphs
• Entanglement and interaction in a topological quantum walk
• Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states
• One-Dimensional Lazy Quantum walk in Ternary System
• Decoherence on a two-dimensional quantum walk using four- and two-state particle
• Dirac equation with ultraviolet cutoff and quantum walk
• Edge states in a two-dimensional quantum walk with disorder
• Transport and Entanglement Generation in the Bose-Hubbard Model
• Conditional Probability Distributions of Finite Absorbing Quantum Walks
• General condition of quantum teleportation by one-dimensional quantum walks
• Single-point position and transition defects in continuous time quantum walks
• Random-walk topological transition revealed via electron counting
• Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems
• Anyonic Quantum Walks
• Maximal coin-walker entanglement in a ballistic quantum walk
• Probing the sign of on-site Hubbard interaction by two-particle quantum walks
• Localization and Recurrence of Quantum Walk in Periodic Potential on a Line
• Multi-qubit quantum computing using discrete-time quantum walks on closed graphs
• Driven Discrete Time Quantum Walks
• From Disordered Quantum Walk to Physics of Off-diagonal Disorder
• Quantum search with interacting Bose-Einstein condensates
• Evanescence in Coined Quantum Walks
• One-Dimensional Quantum Walks with a Position-Dependent Coin
• Quantum simulation of topologically protected states using directionally unbiased linear-optical multiports
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure
• Quantum walks with quantum chaotic coins: Of the Loschmidt echo, classical limit and thermalization
• Floquet engineering of continuous-time quantum walks: towards the simulation of complex and next-to-nearest neighbor couplings
• Invariance in quantum walks with time-dependent coin operators
• Optimization by a quantum reinforcement algorithm
• The Lackadaisical Quantum Walker is NOT Lazy at all
• Improved Upper Bounds for the Hitting Times of Quantum Walks
• Quantum ratchet in disordered quantum walk
• Sub-ballistic behaviour of the Quantum Kicked Rotor
• Out-of-time-ordered correlators and quantum walks
• Parrondo's effect in continuous-time quantum walks
• Using Hilbert transform and classical chains to simulate quantum walks
• Quantum Optical Random Walk: Quantization Rules and Quantum Simulation of Asymptotics
• Understanding and controlling N-dimensional quantum walks via dispersion relations. Application to the 2D and 3D Grover walks: Diabolical points and more
• Unveiling and exemplifying the unitary equivalence of discrete time quantum walk models
• Quantum walker as a probe for its coin parameter
• Classes of random walks on temporal networks with competing timescales
• Quantum walk on the Bloch sphere
• The uniform measure for quantum walk on hypercube: a quantum Bernoulli noises approach
• Unusual scaling in a discrete quantum walk with random long range steps
• Quantum percolation in quasicrystals using continuous-time quantum walk
• Rogue waves in discrete-time quantum walks
• Probability distributions for Markov chains based quantum walks
• Generic quantum walk using a coin-embedded shift operator
• Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks
• Swift chiral quantum walks
• Spatial Search Algorithms on Hanoi Networks
• The quantum walk search algorithm: Factors affecting efficiency
• Discrete dynamics and non-Markovianity
• Localization of discrete time quantum walks on the glued trees
• Dynamics of discrete-time quantum walk with time-correlated unitary noise
• Green function approach for scattering quantum walks
• Interacting quantum walk on a graph
• Non-equilibrium transition from dissipative quantum walk to classical random walk
• Dynamic conditioning of two particle discrete-time quantum walks
• Almost compact moving breathers with fine-tuned discrete time quantum walks
• Lazy Open Quantum Walks
• Complete classification of trapping coins for quantum walks on the 2D square lattice
• Spontaneous Emission in Quantum Walks of a Kicked Bose-Einstein Condensate
• Correlated Markov Quantum Walks
• Quantum walks of interacting Mott insulator defects with three-body interactions
• Noise-enhanced quantum transport on a closed loop using quantum walks
• Symmetry and localization of quantum walk induced by extra link in cycles
• New Developments in Quantum Algorithms
• Quantum random walks on congested lattices
• Two component quantum walk in one-dimensional lattice with hopping imbalance
• Quantum walk, entanglement and thermodynamic laws
• Controlled quantum search on structured databases
• Long-lived quantum speedup based on plasmonic hot spot systems
• Non-classical measurement statistics induced by a coherent spin environment
• Asymptotics of Quantum Random Walk Driven by Optical Cavity
• 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
• Simple derivation of the Weyl and Dirac quantum cellular automata
• Bounds for mixing time of quantum walks on finite graphs
• Quantum State Discrimination on Reconfigurable Noise-Robust Quantum Networks
• Nonlinear flip-flop quantum walks through potential barriers
• Quantum random walk : effect of quenching
• Tunable Aharonov-Bohm-like cages for quantum walks
• Symmetry Protected Topological Phases and Majorana Mode in One-dimensional Quantum Walk with Boundary
• Robust quantum state engineering through coherent localization in biased-coin quantum walks
• Ramsauer effect in one-dimensional quantum walk with multiple defects
• Enhancing the efficiency of quantum annealing via reinforcement: A path-integral Monte Carlo simulation of the quantum reinforcement algorithm
• Multiple Network Alignment on Quantum Computers
• Quantization and Asymptotic Behaviour of ${\epsilon }_{V^k}$ Quantum Random Walk on Integers
• Flux induced re-entrant dynamics in the quantum walk of interacting bosons
• Topological transition of a non-Markovian dissipative quantum walk
• The walker speaks its graph: global and nearly-local probing of the tunnelling amplitude in continuous-time quantum walks
• Analytical results for the Quantum Alternating Operator Ansatz with Grover Mixer
• Quantum walk on a graph of spins: magnetism and entanglement
• Implementation of the quantum walk step operator in lateral quantum dots
• Quantum walks accompanied by spin flipping in one-dimensional optical lattices
• Parrondo's paradox in quantum walks with inhomogeneous coins
• Discrete time Dirac quantum walk in 3+1 dimensions
• Grover Walks on a Line with Absorbing Boundaries
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Quantum walk with a general coin: Exact solution and asymptotic properties
• Quantum Markov Chains on the Comb graphs: Ising model
• Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Driven Gaussian quantum walks
• Second-order topological insulator in a coinless discrete-time quantum walk
• Transient temperature and mixing times of quantum walks on cycles
• Bloch-like energy oscillations
• Quantum walks in polycyclic aromatic hydrocarbons
• Single-photon description of the lossless optical Y coupler
• Quantum Walk Search through Potential Barriers
• Topological classification of time-asymmetry in unitary quantum processes
• Encoding qubits into harmonic-oscillator modes via quantum walks in phase space
• Limit theorems for a localization model of 2-state quantum walks
• Spectral Properties of Quantum Walks on Rooted Binary Trees
• Coherent spatial control of wave packet dynamics on quantum lattices
• Eigenvalues of two-state quantum walks induced by the Hadamard walk
• Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
• Single-qubit unitary gates by graph scattering
• Doubling the Success of Quantum Walk Search Using Internal-State Measurements
• Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning
• Discrete-time quantum walk dispersion control through long-range correlations
• Thermal state entanglement entropy on a quantum graph
• Quantum search in many-body interacting system with long-range interaction
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Pseudo-Hermitian continuous-time quantum walks
• Role of symmetry in quantum search via continuous-time quantum walk
• Entanglement transfer via Chiral Quantum Walk on a Triangular Chain
• Central limit theorems for open quantum random walks on the crystal lattices
• Relative homotopy approach to topological phases in quantum walks
• Pure Phase Decoherence in a Ring Geometry
• Quantum Walks on the Line with Phase Parameters
• The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles
• Microscopic derivation of open quantum walk on two node graph
• Addressable quantum gates
• Thermalization of Fermionic Quantum Walkers
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
• Coherent chemical kinetics as quantum walks II: Radical-pair reactions in Arabidopsis thaliana
• Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study
• Unifying quantum spatial search, state transfer and uniform sampling on graphs: simple and exact
• Quantum Corralling
• Effects of disorder on non-unitary $\mathcal{P}\mathcal{T}$ symmetric quantum walks
• Light-cone and local front dynamics of a single-particle extended quantum walk
• Quantum information spreading in a disordered quantum walk
• Quantum walk on a toral phase space
• Topological delocalization in the completely disordered two-dimensional quantum walk
• Implementing arbitrary quantum operations via quantum walks on a cycle graph
• Glued trees algorithm under phase damping
• Experimental Simulation of Bosonic Creation and Annihilation Operators in a Quantum Processor
• One-dimensional quantum walks driven by two-entangled-qubit coins
• On Fermionic walkers interacting with a correlated structured environment
• Resonant quantum kicked rotor with two internal levels
• Quantum random walk in periodic potential on a line
• History Dependent Quantum Walk on the Cycle with an Unbalanced Coin
• Fractional dynamics in the Lévy quantum kicked rotor
• Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices
• Mean hitting times of quantum Markov chains in terms of generalized inverses
• New theory of diffusive and coherent nature of optical wave via a quantum walk
• A model for quantum queue
• Quantum walks on embedded hypercubes: Nonsymmetric and nonlocal cases
• Multi-photon absorption in optical gratings for matter waves
• Discrete-event simulation of quantum walks
• Non-markovianity and bound states in quantum walks with a phase impurity
• High-fidelity state transfer via quantum walks from delocalized states
• Photonic random walks with traps
• Dynamical Phase Transitions in Open Quantum Walks
• Borromean states in discrete-time quantum walks
• Quantum Walks with Non-Orthogonal Position States
• Superdiffusivity of quantum walks: A Feynman sum-over-paths description
• Fermionic walkers driven out of equilibrium
• n-Qubit Operations on Sphere and Queueing Scaling Limits for Programmable Quantum Computer
• A strange weak value in spontaneous pair productions via a supercritical step potential
• Spectral Properties of Non-Unitary Band Matrices
• Quantum Electrodynamics from Quantum Cellular Automata, and the Tension Between Symmetry, Locality and Positive Energy
• Short time behavior of continuous time quantum walks on graphs
• Quantum Search Algorithms on Hierarchical Networks
• Quantum walk processes in quantum devices
• History states of one-dimensional quantum walks
• Anomalous transport in periodic photonic chains with designed loss
• Resource Reduction in Multiplexed High-Dimensional Quantum Reed-Solomon Codes
• Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs
• Universal dynamical scaling laws in three-state quantum walks
• Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
• Clifford algebra from quantum automata and unitary Wilson fermions
• Quantum spatial search with electric potential : long-time dynamics and robustness to noise
• Nonclassical oscillations in pre- and post-selected quantum walks
• Scattering Expansion for Localization in One Dimension: from Disordered Wires to Quantum Walks
• Quantum Stochastic Walk Models for Quantum State Discrimination
• Practical implementation of a quantum backtracking algorithm
• Quantum Walk on Orbit Spaces
• Trace formulas for general Hermitian matrices: Unitary scattering approach and periodic orbits on an associated graph
• A simple coin for a $2d$ entangled walk
• Hitting time for quantum walks of identical particles
• Strong convergence of quantum random walks via semigroup decomposition
• Effect of the readout efficiency of quantum measurement on the system entanglement
• On the potential of quantum walks for modeling financial return distributions
• Quantum walks and entanglement in cavity networks
• Quantum transport in randomized quantum graphs
• Hitting statistics from quantum jumps
• Spin-1 Quantum Walks
• Quantum centipedes: collective dynamics of interacting quantum walkers
• Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs
• Quantum law of large numbers for Banach spaces
• Quantum correlations and coherence between two particles interacting with a thermal bath
• Weak limits for quantum walks on the half-line
• Non-Markovianity over ensemble averages in quantum complex networks
• Continuous-time quantum walk on integer lattices and homogeneous trees
• Quantum State Transfer through Noisy Quantum Cellular Automata
• On the Power of Weak Measurements in Separating Quantum States
• Behavior of the current in the asymmetric quantum multibaker map
• Phase space patterns of quantum transport on ordered and disordered networks
• Cooling ultracold bosons in optical lattices by spectral transform
• Correlation effects in a discrete quantum random walk
• Photonic cellular automaton simulation of relativistic quantum fields: observation of Zitterbewegung
• Directivity of quantum walk via its random walk replica
• Scattering Expansion for Localization in One Dimension
• Influence of coin symmetry on infinite hitting times in quantum walks
• On Hitting Times for General Quantum Markov Processes
• Dynamics and computation in linear open quantum walks
• Quantum Ultra-Walks: Walks on a Line with Hierarchical Spatial Heterogeneity
• Analytical solutions for quantum walks on 1D chain with different shift operators
• Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles
• Spontaneous-emission induced ratchet in atom-optics kicked rotor quantum walks
• Quantum vs Classical Birth and Death Processes; Exactly Solvable Examples
• Quantum Software Ecosystem Design
• Quantum simulations of complex systems
• Escaping Local Minima with Quantum Coherent Cooling
• Effective simulation of state distribution in qubit chains
• Disorder-free localisation in continuous-time quantum walks : Role of symmetries
• Free Energy on a Cycle Graph and Trigonometric Deformation of Heat Kernel Traces on Odd Spheres
• Interference-induced localization in quantum random walk on clean cyclic graph
• Unidirectional quantum walk of two correlated particles: Separating bound-pair and unbound wavepacket components
• Discrete time quantum walk of locally interacting walkers
• Bath-induced correlations in an infinite-dimensional Hilbert space
• Quantum walks on hypergraphs
• Deterministic generation of hybrid entangled states using quantum walks
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality
• Quantum transport in a combined kicked rotor and quantum walk system
• Renormalization of Discrete-Time Quantum Walks with non-Grover Coins
• Bose-Einstein Condensate Dark Matter That Involves Composites
• Quantum walk for SU(1,1)
• Local Probability Conservation in Discrete Time Quantum Walks
• Spectral Property of Magnetic Quantum Walk on Hypercube
• Quantum walk on a square lattice with identical particles
• Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
• A Flux-Tunable Discrete Angular Filter
• Quantum Paths: a Quantum Walk approach
• The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces
• Quantum Magic in Discrete-Time Quantum Walk
• Improving quantum walk metrology with split-step quantum walk
• Decoherence and classicalization of continuous-time quantum walks on graphs
• Quantum walk with coherent multiple translations induces fast quantum gate operations
• Dynamical Localization and Transport properties of Quantum Walks on the hexagonal lattice
• Conserved Quantities in Linear and Nonlinear Quantum Search
• Clustering-induced localization of quantum walks on networks
• Bosonic Entanglement and Quantum Sensing from Energy Transfer in two-tone Floquet Systems
• Invariance in Quantum Walks
• Repeated measurements and random scattering in quantum walks
• Linear-optical approach to encoding qubits into harmonic-oscillator modes via quantum walks
• Realizing non-trivial doublon formation using a quantum computer
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems
• Superior Exploration-Exploitation Balance with Quantum-Inspired Hadamard Walks
• Quantum random walks on a beam splitter array
• Influence of generic quantum coins on the spreading and entanglement in binary aperiodic quantum walks
• On the nonlinearity of quantum dynamical entropy
• Robustness of random-control quantum-state tomography
• Exciton propagation via quantum walks based on non-Hermitian coin flip operations
• Optimization for the propagation of a multiparticle quantum walk in a one-dimensional lattice
• Robust Quantum Circuit for Clique Problem with Intermediate Qudits
• Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit-qudit dynamics
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Masked states of an atom coupled to a standing-wave cavity mode
• Implementing Quantum Gates Using Length-3 Dynamic Quantum Walks
• An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem
• The Hamiltonians generating one-dimensional discrete-time quantum walks
• Skeleton structure inherent in discrete-time quantum walks
• Revisiting quantum walk advantages: A mean hitting time perspective
• Next-generation interferometry with gauge-invariant linear optical scatterers
• Spectral quantization of discrete random walks on half-line, and orthogonal polynomials on the unit circle
• Bifurcation Curves of Two-Dimensional Quantum Walks
• Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous
• Absorption-based qubit estimation in discrete-time quantum walks
• Crystalline Spectral Form Factors
• Deterministic linear-optical computing with symmetry-based qubits
• Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model
• Cloud-Assisted Contracted Simulation of Quantum Chains
• Temporal nonclassicality in continuous-time quantum walks
• A Generalized Quantum Optical Scheme for Implementing Open Quantum Walks
• Scattering entropies of quantum graphs with several channels
• Topology identification of autonomous quantum dynamical networks
• Quantum Walker in Presence of a Moving Detector
• Protocol for autonomous rearrangement of cold atoms into low-entropy configurations
• Transition in Splitting Probabilities of Quantum Walks
• Light-shift induced behaviors observed in momentum-space quantum walks
• Quantum centipedes with strong global constraint
• Monte Carlo particle transport on quantum computers
• Quantum state transfer and periodicity in discrete-time quantum walks under non--Markovian dephasing noise
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks
• Faster Search of Clustered Marked States with Lackadaisical Quantum Walks
• Quantum spatial best-arm identification via quantum walks
• Kinematics and Dynamics of Quantum Walks in terms of Systems of Imprimitivity
• A group structure arising from Grover walks on complete graphs with self-loops and its application
• Hybrid atom-molecule quantum walks in one-dimensional optical lattice
• Response to glassy disorder in coin on spread of quantum walker
• Finite-size scaling properties of classical random walk on various two-dimensional lattices
• Localized states in monitored quantum walks
• Optimal detection of quantum states via projective measurements