Complex Systems
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
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
Strengths and Weaknesses of Quantum Computing
SIAM Journal on 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
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
Quantum Walks on the Hypercube
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
An Analysis of Absorbing Times of Quantum Walks
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Quantum Random Walks in One Dimension
Quantum Information Processing
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
On the Digraph of a Unitary Matrix
SIAM Journal on Matrix Analysis and Applications
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
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Concise Guide to Complex Hadamard Matrices
Open Systems & Information Dynamics
Optimal computation with non-unitary quantum walks
Theoretical Computer Science
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
Quantum walks on directed graphs
Quantum Information & Computation
Universal mixing of quantum walk on graphs
Quantum Information & Computation
Mixing of quantum walk on circulant bunkbeds
Quantum Information & Computation
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
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
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
One dimensional quantum walks with memory
Quantum Information & Computation
Localization of quantum walks on a deterministic recursive tree
Quantum Information & Computation
Limit theorems for quantum walks with memory
Quantum Information & Computation
Universal mixing of quantum walk on graphs
Quantum Information & Computation
Quantum Information & Computation
Maximal entanglement from quantum random walks
Quantum Information Processing
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
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
Time averaged distribution of a discrete-time quantum walk on the path
Quantum Information Processing
Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
Quantum Information Processing
Limit theorems for decoherent two dimensional quantum walks
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
Decoherence in quantum Markov chains
Quantum Information Processing
| Hi-index | 0.01 |
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, has led rapidly to several new quantum algorithms. These all follow a unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.