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  • Open Access

Benincasa-Dowker-Glaser causal set actions by quantum counting

Sean A. Adamson* and Petros Wallden†

  • *Contact author: sean.adamson@ed.ac.uk
  • †Contact author: petros.wallden@ed.ac.uk
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Phys. Rev. Research 8, 023188 – Published 20 May, 2026

DOI: https://doi.org/10.1103/qdst-yrh6

Abstract

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 Õ(n2) 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(n2)-size arbitrary subset of computational basis states encoding the classical description of a causal set of interest. We then construct depth Õ(n)-depth 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.

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Phys. Rev. Research 8, 023188– Published 20 May, 2026
  • Received 17 June 2025
  • Accepted 11 February 2026
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