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  • Letter
  • Open Access

Single-shot and measurement-based quantum error correction via fault complexes

Timo Hillmann1,2,*, Guillaume Dauphinais1, Ilan Tzitrin1,†, and Michael Vasmer1,3,4

  • *Contact author: timo.hillmann@rwth-aachen.de
  • †Contact author: ilan@xanadu.ai
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Phys. Rev. A 112, L040401 – Published 9 October, 2025

DOI: https://doi.org/10.1103/cjb4-l57n

Abstract

Photonics provides a viable path to a scalable fault-tolerant quantum computer. The natural framework for this platform is measurement-based quantum computation, where fault-tolerant graph states supersede traditional quantum error-correcting codes. However, the existing formalism for foliation—the construction of fault-tolerant graph states—does not reveal how certain properties, such as single-shot error correction, manifest in the measurement-based setting. We introduce the fault complex, a representation of dynamic quantum error-correction protocols particularly well suited to describe foliation. Our approach enables precise computation of fault tolerance properties of foliated codes and provides insights into circuit-based quantum computation. Analyzing the fault complex yields improved thresholds for three- and four-dimensional toric codes, a generalization of stability experiments, and the existence of single-shot lattice surgery with higher-dimensional topological codes.

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Outline

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Phys. Rev. A 112, L040401– Published 9 October, 2025
  • Received 11 November 2024
  • Revised 22 April 2025
  • Accepted 16 September 2025
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