Quantum Gibbs Sampling Using Szegedy Operators

Robert R. Tucci

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arXiv · 0910.1647

Quantum Gibbs Sampling Using Szegedy Operators

Robert R. Tucci

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Abstract

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 $ε>0$, the algorithm will sample a probability distribution in ${\cal O}(\frac{1}{\sqrtδ})$ steps with precision ${\cal O}(ε)$. Here $δ$ is the distance between the two largest eigenvalue magnitudes of the transition matrix of the Gibbs Markov chain used in the algorithm. It takes ${\cal O}(\frac{1}δ)$ steps to achieve the same precision if one does Gibbs sampling on a classical computer.

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Robert R. Tucci. 2010-01-14. Quantum Gibbs Sampling Using Szegedy Operators. https://arxiv.org/abs/0910.1647

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