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  • Open Access

Quantum algorithm for estimating Olivier-Ricci curvature

Nhat A. Nghiem1,2,*, Linh Nguyen3,†, Tuan K. Do4,‡, Tzu-Chieh Wei1,2,§, and Trung V. Phan5,∥

  • *Contact author: nhatanh.nghiemvu@stonybrook.edu
  • †Contact author: linh.nguyen@famu.edu
  • ‡Contact author: ktdo@ucsb.edu
  • §Contact author: tzu-chieh.wei@stonybrook.edu
  • ∥Contact author: tphan@natsci.claremont.edu
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Phys. Rev. Research 8, 023207 – Published 26 May, 2026

DOI: https://doi.org/10.1103/hj52-lksk

Abstract

We introduce a quantum algorithm for computing the Ollivier-Ricci curvature, a discrete analog of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from signaling fragility in financial networks to serving as basic quantities in combinatorial quantum gravity. For inputs given as a point cloud with pairwise distances, we show that our algorithm can achieve an exponential speedup over the best-known classical methods for two particular classes of problems. Our work is another step toward quantum algorithms for geometrical problems that are capable of delivering practical value while also informing fundamental theory.

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Phys. Rev. Research 8, 023207– Published 26 May, 2026
  • Received 13 December 2025
  • Accepted 3 May 2026
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