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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.13681 |
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| _version_ | 1866913510496141312 |
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| author | Grans-Samuelsson, Linnea Aasen, David Bonderson, Parsa |
| author_facet | Grans-Samuelsson, Linnea Aasen, David Bonderson, Parsa |
| contents | We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of pairwise Pauli measurements, with a syndrome extraction circuit of depth 28. We describe fault-tolerant logical operations on patches of this eight-qubit code that generate the full Clifford group. We estimate the performance under circuit noise both during logical idle and during a logical two-qubit measurement. We estimate the pseudo-threshold to be between $10^{-5}$ and $2\times 10^{-4}$, depending on the amount of noise on idle physical qubits. The use of post-selection in addition to error correction (correcting all degree one faults and rejecting a subset of the higher degree faults) can improve the pseudo-threshold by up to an order of magnitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fault-tolerant pairwise measurement-based code on eight qubits Grans-Samuelsson, Linnea Aasen, David Bonderson, Parsa Quantum Physics We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of pairwise Pauli measurements, with a syndrome extraction circuit of depth 28. We describe fault-tolerant logical operations on patches of this eight-qubit code that generate the full Clifford group. We estimate the performance under circuit noise both during logical idle and during a logical two-qubit measurement. We estimate the pseudo-threshold to be between $10^{-5}$ and $2\times 10^{-4}$, depending on the amount of noise on idle physical qubits. The use of post-selection in addition to error correction (correcting all degree one faults and rejecting a subset of the higher degree faults) can improve the pseudo-threshold by up to an order of magnitude. |
| title | A fault-tolerant pairwise measurement-based code on eight qubits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.13681 |