Quantum Bayesian inference: an exploration

Jon Frost, Carlos Madeira, Yash Rastogi and Harald Uhlig ()

No 1342, BIS Working Papers from Bank for International Settlements

Abstract: This paper introduces a framework for performing Bayesian inference using quantum computation. It presents a proof-of-concept quantum algorithm that performs posterior sampling. We provide an accessible introduction to quantum computation for economists and a practical demonstration of quantum-based posterior sampling for Bayesian estimation. Our key contribution is the preparation of a quantum state whose measurement yields samples from a discretised posterior distribution. While the proposed approach does not yet offer computational speedups over classical techniques such as Markov Chain Monte Carlo, it demonstrates the feasibility of simulating Bayesian inference with quantum computation. This work serves as a first step in integrating quantum computation into the econometrician's toolbox. It highlights both the conceptual promise and practical challenges – especially those related to quantum state preparation – in leveraging quantum computation for Bayesian inference.

Keywords: quantum computing; Bayesian estimator; Bayesian inference; Markov chain Monte Carlo (MCMC) algorithms; Gibbs sampling (search for similar items in EconPapers)
JEL-codes: C11 C20 C30 C50 C60 (search for similar items in EconPapers)
Date: 2026-04
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