Benincasa-Dowker-Glaser causal set actions by quantum counting
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913153534656512 |
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| author | Adamson, Sean A. Wallden, Petros |
| author_facet | Adamson, Sean A. Wallden, Petros |
| contents | Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete while retaining local Lorentz invariance. The Benincasa-Dowker-Glaser action is the causal set equivalent to the Einstein-Hilbert action underpinning Einstein's general theory of relativity. We present a $\tilde{O}(n^{2})$ running-time quantum algorithm to compute the Benincasa-Dowker-Glaser action in arbitrary spacetime dimensions for causal sets with $n$ elements which is asymptotically optimal and offers a polynomial speedup compared to all known classical or quantum algorithms. To do this, we prepare a uniform superposition over an $O(n^{2})$-size arbitrary subset of computational basis states encoding the classical description of a causal set of interest. We then construct depth $\tilde{O}(n)$ oracle circuits testing for different discrete volumes between pairs of causal set elements. Repeatedly performing a two-stage variant of quantum counting using these oracles yields the desired algorithm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_22217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benincasa-Dowker-Glaser causal set actions by quantum counting Adamson, Sean A. Wallden, Petros Quantum Physics General Relativity and Quantum Cosmology Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete while retaining local Lorentz invariance. The Benincasa-Dowker-Glaser action is the causal set equivalent to the Einstein-Hilbert action underpinning Einstein's general theory of relativity. We present a $\tilde{O}(n^{2})$ running-time quantum algorithm to compute the Benincasa-Dowker-Glaser action in arbitrary spacetime dimensions for causal sets with $n$ elements which is asymptotically optimal and offers a polynomial speedup compared to all known classical or quantum algorithms. To do this, we prepare a uniform superposition over an $O(n^{2})$-size arbitrary subset of computational basis states encoding the classical description of a causal set of interest. We then construct depth $\tilde{O}(n)$ oracle circuits testing for different discrete volumes between pairs of causal set elements. Repeatedly performing a two-stage variant of quantum counting using these oracles yields the desired algorithm. |
| title | Benincasa-Dowker-Glaser causal set actions by quantum counting |
| topic | Quantum Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.22217 |