Single-shot and measurement-based quantum error correction via fault complexes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917009799774208 |
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| author | Hillmann, Timo Dauphinais, Guillaume Tzitrin, Ilan Vasmer, Michael |
| author_facet | Hillmann, Timo Dauphinais, Guillaume Tzitrin, Ilan Vasmer, Michael |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Single-shot and measurement-based quantum error correction via fault complexes Hillmann, Timo Dauphinais, Guillaume Tzitrin, Ilan Vasmer, Michael Quantum Physics 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. |
| title | Single-shot and measurement-based quantum error correction via fault complexes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.12963 |