On fault tolerant single-shot logical state preparation and robust long-range entanglement
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916607821873152 |
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| author | Bergamaschi, Thiago Liu, Yunchao |
| author_facet | Bergamaschi, Thiago Liu, Yunchao |
| contents | Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman's clustering-of-errors argument. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On fault tolerant single-shot logical state preparation and robust long-range entanglement Bergamaschi, Thiago Liu, Yunchao Quantum Physics Strongly Correlated Electrons Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman's clustering-of-errors argument. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement. |
| title | On fault tolerant single-shot logical state preparation and robust long-range entanglement |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.04405 |