量子贝叶斯推理：一种探索

Quantum Bayesianinference: an exploration by Jon Frost, Carlos Madeira, Yash Rastogi and HaraldUhlig Monetary and Economic Department April2026 JEL classification: C11, C20, C30, C50, C60 Keywords:Quantum computing,Bayesian estimator,Bayesian inference, Markov chain Monte Carlo (MCMC)algorithms, Gibbs sampling BISWorking Papers are written by members of the Monetary and EconomicDepartment of the Bank for International Settlements, and from time to time by othereconomists, and are published by the Bank. The papers are on subjects of topicalinterest and are technical in character. The views expressed in this publication arethose of the authors and do not necessarily reflect the views of the BIS or its membercentral banks. This publication is available on the BIS website (www.bis.org). Quantum Bayesian Inference: An Exploration Jon Frost, Carlos Madeira, Yash Rastogi and Harald Uhlig∗ First draft: July 21, 2025This revision: February 20, 2026 Abstract This paper introduces a framework for performing Bayesian infer-ence using quantum computation. It presents a proof-of-concept quan-tum algorithm that performs posterior sampling. We provide an acces-sible introduction to quantum computation for economists and a prac-tical demonstration of quantum-based posterior sampling for Bayesianestimation.Our key contribution is the preparation of a quantumstate whose measurement yields samples from a discretized posteriordistribution.While the proposed approach does not yet offer com-putational speedups over classical techniques such as Markov ChainMonte Carlo, it demonstrates the feasibility of simulating Bayesian in-ference with quantum computation. This work serves as a first step inintegrating quantum computation into the econometrician’s toolbox.It highlights both the conceptual promise and practical challenges—especially those related to quantum state preparation—in leveragingquantum computation for Bayesian inference. Keywords: Quantum computing; Bayesian estimator; Bayesianinference; Markov chain Monte Carlo (MCMC) algorithms; Gibbssampling JEL codes: C11; C20; C30; C50; C60 1Introduction This paper explores the potential of quantum computation as a framework forBayesian inference. Quantum bits (qubits) are probabilistic objects, makingquantum computation conceptually aligned with Bayesian inference, wherebelief updates are driven by probabilistic rules.This conceptual parallelmotivates our key idea:encoding a discretized posterior distribution over2npossible parameter values into the amplitudes of ann-qubit state, andusing quantum measurement to sample from this distribution.In effect,we propose using quantum computation as a means for sampling from theposterior distribution in Bayesian inference. In practice, quantum computation is a field largely driven forward byengineers and computer scientists, while statisticians and econometriciansstudy Bayesian inference.Bridging this disciplinary divide requires trans-lating core ideas across fields. To that end, we provide an accessible intro-duction to quantum computation tailored to economists, alongside a concisereview of Bayesian inference. We then present a simple quantum workflowfor posterior sampling and implement it using the Qiskit package in thePython programming language.Although our method does not currentlyoffer computational advantages over classical techniques, our primary aimis conceptual: to demonstrate the feasibility of using quantum computationto perform Bayesian inference and lay a foundation for future algorithmicinnovations that may realize quantum speedups. Despite the early excitement surrounding quantum computation, the fieldremains in its infancy when it comes to solving computationally intense prob-lems at scale. Progress has been constrained by significant engineering chal-lenges, including qubit decoherence, error correction, and hardware scala-bility.Many quantum algorithms offer exponential speedups over classicalalgorithms in theory but have not yet been demonstrated at scale in practice due to the current limitations in quantum hardware.1For example, numberfactorization using Shor’s algorithm so far has been limited to small numbers,since quantum computing remains noisy and only operates at intermediatescale (Mart´ın-L´opez et al.2012 [16]).2 Only recently has a quantum com-puter been built that is able to run for longer than 2 hours (Chiu et al. 2025[6]). Some critics have questioned whether quantum advantage will ever beachieved at scale due to the computational requirements for noise-reductionas exercises scale up (Kalai 2020 [13]).Even optimistic assessments sug-gest that demonstrable speedups may remain elusive for applied problems ofeconomic relevance (Hoefler et al. 2023 [12]). Despite these diverging views, however, some quantum computing devel-opers believe that significant advances will be made for the study of molec-ular reactions, materials research and maybe for some managerial processessuch as logistics