Quantum Gibbs Sampling Using Szegedy Operators

Details Quantum Gibbs Sampling Using Szegedy Operators Quantum Gibbs Sampling Using Szegedy Operators

2009-10-09

arxiv.org/abs/0910.1647v2

Physics

Quantum Physics

V1-17 pages(8 files:1 .tex, 2 .sty, 5 .eps);V2-many minor changes to improve larity

Scientific paper

We present an algorithm for doing Gibbs sampling on a quantum computer. The algorithm combines phase estimation for a Szegedy operator, and Grover's algorithm. For any $\epsilon>0$, the algorithm will sample a probability distribution in ${\cal O}(\frac{1}{\sqrt{\delta}})$ steps with precision ${\cal O}(\epsilon)$. Here $\delta$ is the distance between the two largest eigenvalue magnitudes of the transition matrix of the Gibbs Markov chain used in the algorithm. It takes ${\cal O}(\frac{1}{\delta})$ steps to achieve the same precision if one does Gibbs sampling on a classical computer.

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