Quantum Inference on Bayesian Networks

TL;DR

This paper introduces a quantum algorithm for inference in Bayesian networks that achieves a quadratic speedup over classical methods by utilizing quantum rejection sampling and amplitude amplification, without relying on blackbox oracles.

Contribution

The authors develop a quantum rejection sampling method for Bayesian networks that provides a square-root speedup in inference tasks, leveraging the network's structure for efficient quantum state preparation.

Findings

Quantum rejection sampling achieves a quadratic speedup.

The method constructs a quantum state representing the distribution efficiently.

No blackbox oracle queries are needed for the speedup.

Abstract

Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $\mathcal{O}(nmP(e)^{-1})$, depending critically on $P(e)$, the probability the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $\mathcal{O}(n2^mP(e)^{-\frac12})$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized -- we count primitive operations and require no blackbox oracle queries.