A. Sinclair and M. Jerrum. Approximate counting, uniform generation, and rapidly mixing markov chains. Inform. and Comput., 82:93-113, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....j 0 i; j 0 i as initial states. Denote by P t ; P t the induced distributions of j t i; j t i on the nodes of the graph. Clearly, k P T P T k max t T kP t P t k. Due to unitarity of the walk, the distance is preserved: kj t i j t ik = kj 0 i j 0 ik. By lemma 11 in [9], the total variation distance between the two probability distributions resulting from a measurement on two states which are apart, is at most 2 . This proves the claim. 2 Claim 4.10 Let j 0 i be the initial basis state, and j 0 i be the initial basis state projected on the good ....

A. Sinclair and M. Jerrum, Approximate counting, generation, and rapidly mixing Markov chains, in Information and Computation, 82, 1989, pages 93-133. 16

....G of the graph with vertices G be de ned as CX = X s2X s FX = X u2X;v62X p u;v u : 2) where is the stationary distribution, and p u;v is the transition probability. Then the conductance is = min 0 jXj jGj CX 1=2 FX CX (3) Theorem 2 Conductance and spectral gap: Jerrum, Sinclair[7]] 2 2 (1 2 ) 2 (4) Example It is well known that for the simple random walk on an n cycle, the mixing time is quadratic, S = n 2 log(1= and so are the lling time and the dispersion time. 2.2 Quantum Computation The model. Consider a nite Hilbert space H with an ....

A. Sinclair and M. Jerrum, approximate counting, generation, and rapidly mixing Markov chains, in information and computation, 82, 1989, pages 93-133.

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A. Sinclair and M. Jerrum. Approximate counting, uniform generation, and rapidly mixing markov chains. Inform. and Comput., 82:93-113, 1989.

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