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

• URL: http://arxiv.org/abs/2506.19538v1
• Date: Tue, 24 Jun 2025 11:47:02 GMT
• Title: Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo
• Authors: Stuart Ferguson, Arad Nasiri, Petros Wallden,
• Abstract summary: Causal Set Theory is a discrete, Lorentz-invariant approach to quantum gravity.<n>We introduce a quantum algorithm that investigates the dynamics of causal sets by sampling the space of causal sets.
• Score: 0.8192907805418583
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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