1. Single-shot and measurement-based quantum error correction via fault complexes
- Author
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Hillmann, Timo, Dauphinais, Guillaume, Tzitrin, Ilan, and Vasmer, Michael
- Subjects
Quantum Physics - 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., Comment: 13 pages, 5 figures
- Published
- 2024