Randomized algorithms
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
An introduction to quantum computing for non-physicists
ACM Computing Surveys (CSUR)
Quantum simulations of classical random walks and undirected graph connectivity
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Feynman Lectures on Computation
Feynman Lectures on Computation
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
Quantum Walks on the Hypercube
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Quantum Random Walks in One Dimension
Quantum Information Processing
Quantum Information Processing
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Classical and Quantum Computation
Classical and Quantum Computation
Quantum Search of Spatial Regions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Improving Gate-Level Simulation of Quantum Circuits
Quantum Information Processing
ACM SIGACT News
Towards a quantum programming language
Mathematical Structures in Computer Science
Asymptotics of Multivariate Sequences II: Multiple Points of the Singular Variety
Combinatorics, Probability and Computing
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
One-dimensional quantum walks with absorbing boundaries
Journal of Computer and System Sciences
Coins make quantum walks faster
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Functional Quantum Programming Language
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A structural approach to reversible computation
Theoretical Computer Science
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to Quantum Information Science (Oxford Graduate Texts)
Introduction to Quantum Information Science (Oxford Graduate Texts)
Protecting Information: From Classical Error Correction to Quantum Cryptography
Protecting Information: From Classical Error Correction to Quantum Cryptography
Quantum Computing and Communications: An Engineering Approach
Quantum Computing and Communications: An Engineering Approach
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Complexity of Testing Group Commutativity
Algorithmica
Computing with a trillion crummy components
Communications of the ACM - ACM's plan to go online first
Computation with carbon nanotube devices
Communications of the ACM - ACM's plan to go online first
Molecular, chemical, and organic computing
Communications of the ACM - ACM's plan to go online first
Autonomous programmable biomolecular devices using self-assembled DNA nanostructures
Communications of the ACM - ACM's plan to go online first
Toward a world with quantum computers
Communications of the ACM - ACM's plan to go online first
Optical computing: need and challenge
Communications of the ACM - ACM's plan to go online first
Communications of the ACM - ACM's plan to go online first
Amoeba-based neurocomputing with chaotic dynamics
Communications of the ACM - ACM's plan to go online first
Quantum Computer Science: An Introduction
Quantum Computer Science: An Introduction
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
SIAM Journal on Computing
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
Quantum Algorithms for Hidden Nonlinear Structures
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Symmetry in quantum walks
Explorations in Quantum Computing
Explorations in Quantum Computing
Quantum Algorithms for Evaluating Min-Max Trees
Theory of Quantum Computation, Communication, and Cryptography
Quantum Walks for Computer Scientists
Quantum Walks for Computer Scientists
A Symbolic Classical Computer Language for Simulation of Quantum Algorithms
QI '09 Proceedings of the 3rd International Symposium on Quantum Interaction
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
Quantum computation and image processing: new trends in artificial intelligence
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Recent progress in quantum algorithms
Communications of the ACM
Logical reversibility of computation
IBM Journal of Research and Development
Processing images in entangled quantum systems
Quantum Information Processing
Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory
Quantum Information Processing
Quantum random walks - new method for designing quantum algorithms
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Localization of an inhomogeneous discrete-time quantum walk on the line
Quantum Information Processing
Finding is as easy as detecting for quantum walks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Continuous-time quantum walks on the threshold network model
Mathematical Structures in Computer Science
Quantum walks and elliptic integrals
Mathematical Structures in Computer Science
On the von neumann entropy of certain quantum walks subject to decoherence†
Mathematical Structures in Computer Science
Quantum algorithmic methods for computational geometry
Mathematical Structures in Computer Science
Quantum Information Processing
Strategies for designing geometric transformations on quantum images
Theoretical Computer Science
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
Quantum Computing: A Gentle Introduction
Quantum Computing: A Gentle Introduction
Coalgebraic walks, in quantum and turing computation
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Efficient circuits for quantum walks
Quantum Information & Computation
One dimensional quantum walks with memory
Quantum Information & Computation
Localization of discrete-time quantum walks on a half line via the CGMV method
Quantum Information & Computation
Limit theorems for quantum walks with memory
Quantum Information & Computation
Limit theorems and absorption problems for quantum random walks in one dimension
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
Quantum walks on directed graphs
Quantum Information & Computation
Quantum Information & Computation
Watermarking and authentication of quantum images based on restricted geometric transformations
Information Sciences: an International Journal
Maximal entanglement from quantum random walks
Quantum Information Processing
On the Hitting Times of Quantum Versus Random Walks
Algorithmica
Sojourn times of the Hadamard walk in one dimension
Quantum Information Processing
On the relation between quantum walks and zeta functions
Quantum Information Processing
Spatial search using the discrete time quantum walk
Natural Computing: an international journal
Quantum Radar
Crossovers induced by discrete-time quantum walks
Quantum Information & Computation
Return probability of one-dimensional discrete-time quantum walks with final-time dependence
Quantum Information & Computation
Entanglement for discrete-time quantum walks on the line
Quantum Information & Computation
Perfect state transfer on quotient graphs
Quantum Information & Computation
Limit theorems for the discrete-time quantum walk on a graph with joined half lines
Quantum Information & Computation
Dynamical localization for d-dimensional random quantum walks
Quantum Information Processing
Time averaged distribution of a discrete-time quantum walk on the path
Quantum Information Processing
Asymptotic distributions of quantum walks on the line with two entangled coins
Quantum Information Processing
Enhancing the spreading of quantum walks on star graphs by additional bonds
Quantum Information Processing
Hitting time of quantum walks with perturbation
Quantum Information Processing
Limit measures of inhomogeneous discrete-time quantum walks in one dimension
Quantum Information Processing
Decoherence in quantum Markov chains
Quantum Information Processing
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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 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.