Bayesian Inference in Quantum Programs
Abstract
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also known as Bayesian inference. This paper equips a quantum while-language with conditioning, defines its denotational and operational semantics over infinite-dimensional Hilbert spaces, and shows their equivalence. We provide sufficient conditions for the existence of weakest (liberal) precondition-transformers and derive inductive characterizations of these transformers. It is shown how w(l)p-transformers can be used to assess the effect of Bayesian inference on (possibly diverging) quantum programs.
Cite
@article{arxiv.2504.20732,
title = {Bayesian Inference in Quantum Programs},
author = {Christina Gehnen and Dominique Unruh and Joost-Pieter Katoen},
journal= {arXiv preprint arXiv:2504.20732},
year = {2025}
}
Comments
This is the full version of the paper "Bayesian Inference in Quantum Programs" appearing at ICALP 2025