Quantum Bayesian inference: an exploration
Summary
Focus
We explore how quantum computation – a computing method based on the principles of quantum physics – could be applied to Bayesian inference – an approach to updating beliefs and making predictions based on prior knowledge and new data. While quantum computing is being driven forward by engineers and computer scientists, it is statisticians and econometricians who study Bayesian inference. Bridging this disciplinary divide requires translating core ideas across fields.
Contribution
We briefly explain quantum computation for economists. We then present a proof-of-concept quantum algorithm that performs posterior sampling, ie a step-by-step process for estimating possible outcomes based on new data and prior knowledge. We do so by showing code listings using the Qiskit package in the Python programming language. Our algorithm uses quantum properties to represent the updated probabilities and generate random samples for Bayesian inference.
Findings
Quantum computing is still at an early stage. In principle, there is great promise for new computational achievements, and advances in hardware and quantum algorithms may have applications for logistics, portfolio management and business cycle modelling. Our approach demonstrates the feasibility of doing Bayesian inference with quantum computation simulation. But importantly, our method does not yet offer faster computation than classical techniques such as Markov Chain Monte Carlo, importance sampling or particle filtering. This remains an area for future research.
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.
JEL classification: C11, C20, C30, C50, C60
Keywords: quantum computing; Bayesian estimator; Bayesian inference; Markov chain Monte Carlo (MCMC) algorithms; Gibbs sampling
