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• W4385340982 abstract "The Markov chain Monte Carlo (MCMC) method, especially the Metropolis-Hastings (MH) algorithm, is a widely used technique for sampling from a target probability distribution $P$ on a state space $mathrm{ensuremath{Omega}}$ and applied to various problems such as estimation of parameters in statistical models in the Bayesian approach. Quantum algorithms for MCMC have been proposed, yielding the quadratic speedup with respect to the spectral gap $mathrm{ensuremath{Delta}}$ compared to classical counterparts. In this paper, we consider the quantum version of the MH algorithm in the case that calculating $P$ is costly because the log-likelihood $L$ for a state $xensuremath{in}mathrm{ensuremath{Omega}}$ is obtained via computing the sum of many terms, $frac{1}{M}{ensuremath{sum}}_{i=0}^{Mensuremath{-}1}ensuremath{ell}(i,x)$. We propose calculating $L$ by quantum Monte Carlo integration and combine it with the existing method called quantum simulated annealing (QSA) to generate the quantum state that encodes $P$ in amplitudes. We consider not only state generation but also finding a credible interval for a parameter, a common task in Bayesian inference. In the proposed method for credible interval calculation, the number of queries to the quantum circuit to compute $ensuremath{ell}$ scales on $mathrm{ensuremath{Delta}}$, the required accuracy $ensuremath{epsilon}$, and the standard deviation $ensuremath{sigma}$ of $ensuremath{ell}$ as $stackrel{ifmmode tilde{}else ~{}fi{}}{O}(ensuremath{sigma}/{ensuremath{epsilon}}^{2}{mathrm{ensuremath{Delta}}}^{3/2})$, in contrast to $stackrel{ifmmode tilde{}else ~{}fi{}}{O}(M/ensuremath{epsilon}{mathrm{ensuremath{Delta}}}^{1/2})$ for QSA with $L$ calculated exactly. Therefore, the proposed method is advantageous if $ensuremath{sigma}$ scales on $M$ sublinearly. As one such example, we consider parameter estimation in a gravitational wave experiment, where $ensuremath{sigma}=O({M}^{1/2})$." @default.
• W4385340982 created "2023-07-29" @default.
• W4385340982 creator A5069845994 @default.
• W4385340982 date "2023-07-28" @default.
• W4385340982 modified "2023-09-26" @default.
• W4385340982 title "Quantum Metropolis-Hastings algorithm with the target distribution calculated by quantum Monte Carlo integration" @default.
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• W4385340982 doi "https://doi.org/10.1103/physrevresearch.5.033059" @default.
• W4385340982 hasPublicationYear "2023" @default.
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