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arXiv · 2410.12963

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

Timo Hillmann·Guillaume Dauphinais·Ilan Tzitrin·Michael Vasmer
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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 leads to 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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Timo Hillmann, Guillaume Dauphinais, Ilan Tzitrin, Michael Vasmer. 2024-10-16. Single-shot and measurement-based quantum error correction via fault complexes. https://doi.org/10.1103/cjb4-l57n

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