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
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 Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum information processing in continuous time
Quantum information processing in continuous time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Adiabatic Quantum State Generation
SIAM Journal on Computing
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Quantum walks and ground state problems
Quantum walks and ground state problems
Mixing and decoherence in continuous-time quantum walks on cycles
Quantum Information & Computation
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Markov chain Monte Carlo (MCMC) is the widely-used classical method of random sampling from a probability distribution 驴by simulating a Markov chain which "mixes" to 驴at equilibrium. Despite the success quantum walks have been shown to have in speeding up random walk algorithms for search problems ("hitting") and simulated annealing, it remains to prove a general speedup theorem for MCMC sampling algorithms. We review the progress toward this end, in particular using decoherent quantum walks.