Quantum Enhanced Inference in Markov Logic Networks

TL;DR

This paper explores how quantum protocols can significantly accelerate probabilistic inference in Markov logic networks by leveraging their symmetric structures, demonstrating potential quantum advantages in machine learning tasks.

Contribution

It introduces quantum methods for speeding up Gibbs sampling in MLNs, showing exponential speedup over classical heuristics for approximate inference.

Findings

Quantum protocols can exponentially speed up Gibbs sampling in MLNs.

Symmetric structures in MLNs can be exploited by quantum algorithms.

Quantum resources may enhance machine learning inference tasks.

Abstract

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.