Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo

TL;DR

This paper introduces a quantum algorithm based on quantum-enhanced Markov Chain Monte Carlo to efficiently sample causal sets in quantum gravity, achieving super-quadratic scaling advantages over classical methods.

Contribution

It adapts the quantum-enhanced MCMC technique to constrained spaces in causal set theory, incorporating a specific Hamiltonian for quantum gravity applications.

Findings

Achieved super-quadratic quantum scaling advantage

Demonstrated potential for greater efficiency over classical methods

Extended QeMCMC to constrained causal set sampling

Abstract

Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to quantum gravity which may be well positioned to benefit from quantum computing. In this work, we introduce a quantum algorithm that investigates the dynamics of causal sets by sampling the space of causal sets, improving on classical methods. Our approach builds on the quantum-enhanced Markov chain Monte Carlo technique developed by Layden et al. [Nature 619, 282 (2023)], adapting it to sample from the constrained spaces required for application. This is done by adding a constraint term to the Hamiltonian of the system. A qubit Hamiltonian representing the Benincasa-Dowker action (the causal set equivalent of the Einstein-Hilbert action) is also derived and used in the algorithm as the problem Hamiltonian. We achieve a super-quadratic quantum scaling advantage and, under some conditions, demonstrate a greater potential compared to classical approaches than previously observed in unconstrained QeMCMC implementations.