Single-shot and measurement-based quantum error correction via fault complexes
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.
Cite
@article{arxiv.2410.12963,
title = {Single-shot and measurement-based quantum error correction via fault complexes},
author = {Timo Hillmann and Guillaume Dauphinais and Ilan Tzitrin and Michael Vasmer},
journal= {arXiv preprint arXiv:2410.12963},
year = {2025}
}
Comments
15 pages, 6 figures, accepted version