SIAM Journal on Computing
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
The method of creative telescoping
Journal of Symbolic Computation
On asymptotics of Jacobi polynomials
SIAM Journal on Mathematical Analysis
On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Randomized algorithms
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Faster mixing via average conductance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Concrete Math
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A probabilistic analysis of multidimensional bin packing problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
An Analysis of Absorbing Times of Quantum Walks
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
One-Dimensional Continuous-Time Quantum Walks
Quantum Information Processing
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
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Optimal computation with non-unitary quantum walks
Theoretical Computer Science
The Quantum Complexity of Markov Chain Monte Carlo
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Quantum Walks and Quantum Cellular Automata
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
Graph matching using the interference of discrete-time quantum walks
Image and Vision Computing
Coined quantum walks lift the cospectrality of graphs and trees
Pattern Recognition
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory
Quantum Information Processing
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
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
A hybrid classical-quantum clustering algorithm based on quantum walks
Quantum Information Processing
Tree search and quantum computation
Quantum Information Processing
One dimensional quantum walks with memory
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
On mixing in continuous-time quantum walks on some circulant graphs
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
Mixing and decoherence in continuous-time quantum walks on cycles
Quantum Information & Computation
Graph embedding using a quasi-quantum analogue of the hitting times of continuous time quantum walks
Quantum Information & Computation
SIAM Journal on Computing
Maximal entanglement from quantum random walks
Quantum Information Processing
Coined quantum walks lift the cospectrality of graphs and trees
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Spatial search using the discrete time quantum walk
Natural Computing: an international journal
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
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
Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle
Quantum Information Processing
Quantum walks: a comprehensive review
Quantum Information Processing
Mixing-time and large-decoherence in continuous-time quantum walks on one-dimension regular networks
Quantum Information Processing
Limit theorems for the interference terms of discrete-time quantum walks on the line
Quantum Information & Computation
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We define and analyze quantum computational variants of random walks on one-dimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum and classical cases are observed. For example, when unrestricted in either direction, the Hadamard walk has position that is nearly uniformly distributed in the range [-t/\sqrt 2, t/\sqrt 2] after t steps, which is in sharp contrast to the classical random walk, which has distance O(\sqrt t) from the origin with high probability. With an absorbing boundary immediately to the left of the starting position, the probability that the walk exits to the left is 2/&pgr, and with an additional absorbing boundary at location n, the probability that the walk exits to the left actually increases, approaching 1/\sqrt 2 in the limit. In the classical case both values are 1.