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The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems.
Some inequalities for reversible Markov chains
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Inverse M-matrix inequalities and generalized ultrametric matrices. 220, 321 – 341,
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Mixing times for uniformly ergodic Markov chains, 2, 165–185,
Aldous, D. , László, L and Winkler, P · 1995
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Monte Carlo Methods in Statistical Physics , (Oxford University Press, Oxford, UK, 1999)
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Lifting Markov Chains to Speed Up Mixing
Chen, F., Lovász, L. and Pak, I · 1999
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Quantum Amplitude Amplification and Estimation
Brassard, G., Hoyer, P., Mosca, M. and Tapp, A · 2000
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Quantum information processing in continuous time. Ph. D. Thesis, Massachusetts Institute of Technology, (2004)
Childs, A · 2004
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Quantum speed-up of markov chain based algorithms
Szegedy, M · 2004
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Magniez, F., Santha, M. & Szegedy, M · 2005
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Markov chains and mixing times. American Mathematical Society (2006)
Levin, D. A., Peres, Y. and Wilmer, E. L · 2006
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Quantum speedup of classical mixing processes
Richter, P. C · 2007
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Search via quantum walk
Magniez, F., Nayak, A., Roland, J. & Santha, M · 2011
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Quantum walks can find a marked element on any graph
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Quantum speedup for active learning agents
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Quantum mixing for slowly evolving sequences of Markov chains
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