Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912446964301824 |
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| author | Ferguson, Stuart Nasiri, Arad Wallden, Petros |
| author_facet | Ferguson, Stuart Nasiri, Arad Wallden, Petros |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_19538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo Ferguson, Stuart Nasiri, Arad Wallden, Petros Quantum Physics General Relativity and Quantum Cosmology Computational Physics 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. |
| title | Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo |
| topic | Quantum Physics General Relativity and Quantum Cosmology Computational Physics |
| url | https://arxiv.org/abs/2506.19538 |