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  • Open Access

Sub-Riemannian geometry of measurement-based quantum computation

Lukas Hantzko1,*, Arnab Adhikary1,2,3,†, and Robert Raussendorf1,3,‡

  • *Contact author: lukas.hantzko@itp.uni-hannover.de
  • †Contact author: arnab.adhikary@itp.uni-hannover.de
  • ‡Contact author: robert.raussendorf@itp.uni-hannover.de
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Phys. Rev. A 113, 012444 – Published 30 January, 2026

DOI: https://doi.org/10.1103/zq4l-vwbz

Abstract

The computational power of quantum phases of matter with symmetry can be accessed through local measurements, but what is the most efficient way of doing so? In this work we show that minimizing operational resources in measurement-based quantum computation (MBQC) on subsystem symmetric resource states amounts to solving a sub-Riemannian geodesic problem between the identity and the target logical unitary. This reveals a geometric structure underlying MBQC and offers a principled route to optimize quantum processing in computational phases.

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Phys. Rev. A 113, 012444– Published 30 January, 2026
  • Received 9 September 2025
  • Accepted 24 December 2025
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