Flag Gadgets based on Classical Codes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914687094882304 |
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| author | Anker, Benjamin Marvian, Milad |
| author_facet | Anker, Benjamin Marvian, Milad |
| contents | Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computations. While conventional methods use a number of extra qubits linear in the weight of the syndrome, several improvements have been introduced using flag gadgets. In this work, we develop a framework to design flag gadgets using classical codes. Using this framework we show how to perform fault-tolerant syndrome extraction for any stabilizer code with arbitrary distance using exponentially fewer qubits than conventional methods when qubit measurement and reset are relatively slow compared to a round of error correction. We further take advantage of the saving provided by our construction to fault-tolerantly measure multiple stabilizers using a single gadget, and show that it maintains the same exponential advantage when it is used to fault-tolerantly extract the syndrome of quantum LDPC codes. Using the developed framework we perform computer-assisted search to find several small examples where our constructions reduce the number of qubits required. These small examples may be relevant to near-term experiments on small-scale quantum computers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10738 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Flag Gadgets based on Classical Codes Anker, Benjamin Marvian, Milad Quantum Physics Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computations. While conventional methods use a number of extra qubits linear in the weight of the syndrome, several improvements have been introduced using flag gadgets. In this work, we develop a framework to design flag gadgets using classical codes. Using this framework we show how to perform fault-tolerant syndrome extraction for any stabilizer code with arbitrary distance using exponentially fewer qubits than conventional methods when qubit measurement and reset are relatively slow compared to a round of error correction. We further take advantage of the saving provided by our construction to fault-tolerantly measure multiple stabilizers using a single gadget, and show that it maintains the same exponential advantage when it is used to fault-tolerantly extract the syndrome of quantum LDPC codes. Using the developed framework we perform computer-assisted search to find several small examples where our constructions reduce the number of qubits required. These small examples may be relevant to near-term experiments on small-scale quantum computers. |
| title | Flag Gadgets based on Classical Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2212.10738 |