Sub-Riemannian geometry of measurement based quantum computation
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 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.
Cite
@article{arxiv.2508.17808,
title = {Sub-Riemannian geometry of measurement based quantum computation},
author = {Lukas Hantzko and Arnab Adhikary and Robert Raussendorf},
journal= {arXiv preprint arXiv:2508.17808},
year = {2026}
}
Comments
9 pages, 4 figures. This is the Accepted Manuscript version of an article accepted for publication in Phys. Rev. A. The American Physical Society is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. This Accepted Manuscript is published under a CC BY licence. The Version of Record is available online at 10.1103/zq4l-vwbz