Quantum Computer as a Probabilistic Inference Engine

TL;DR

This paper introduces a novel class of quantum algorithms designed to estimate probability distributions, extending classical reversible computing methods to quantum Bayesian networks for improved inference in AI and decision-making.

Contribution

It generalizes the Fredkin-Toffoli construction to quantum Bayesian networks, enabling quantum computation of classical probabilistic inferences, and explores integration with Grover's algorithm for enhanced performance.

Findings

Quantum Bayesian nets can compute conditional probabilities efficiently.

The proposed algorithms generalize classical reversible computing to probabilistic models.

Potential advantages when combined with Grover's algorithm in certain scenarios.

Abstract

We propose a new class of quantum computing algorithms which generalize many standard ones. The goal of our algorithms is to estimate probability distributions. Such estimates are useful in, for example, applications of Decision Theory and Artificial Intelligence, where inferences are made based on uncertain knowledge. The class of algorithms that we propose is based on a construction method that generalizes a Fredkin-Toffoli (F-T) construction method used in the field of classical reversible computing. F-T showed how, given any binary deterministic circuit, one can construct another binary deterministic circuit which does the same calculations in a reversible manner. We show how, given any classical stochastic network (classical Bayesian net), one can construct a quantum network (quantum Bayesian net). By running this quantum Bayesian net on a quantum computer, one can calculate any conditional probability that one would be interested in calculating for the original classical Bayesian net. Thus, we generalize the F-T construction method so that it can be applied to any classical stochastic circuit, not just binary deterministic ones. We also show that, in certain situations, our class of algorithms can be combined with Grover's algorithm to great advantage.