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Abstract: We present an algorithm for doing Gibbs sampling on a quantum computer. Thealgorithm combines phase estimation for a Szegedy operator, and Grover-salgorithm. For any $\epsilon>0$, the algorithm will sample a probabilitydistribution in ${\cal O}\frac{1}{\sqrt{\delta}}$ steps with precision ${\calO}\epsilon$. Here $\delta$ is the distance between the two largest eigenvaluemagnitudes of the transition matrix of the Gibbs Markov chain used in thealgorithm. It takes ${\cal O}\frac{1}{\delta}$ steps to achieve the sameprecision if one does Gibbs sampling on a classical computer.



Author: Robert R. Tucci

Source: https://arxiv.org/



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