Fault-tolerant syndrome extraction and cat state preparation with fewer qubits
We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an exponential reduction in qubit overhead over the previous best p...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-10-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-10-24-1154/pdf/ |
| _version_ | 1797650977977794560 |
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| author | Prithviraj Prabhu Ben W. Reichardt |
| author_facet | Prithviraj Prabhu Ben W. Reichardt |
| author_sort | Prithviraj Prabhu |
| collection | DOAJ |
| description | We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an exponential reduction in qubit overhead over the previous best protocol. For a weight-$w$ stabilizer, we demonstrate that stabilizer measurement tolerating one fault needs at most $\lceil \log_2 w \rceil + 1$ ancilla qubits. If qubits reset quickly, four ancillas suffice. We also study the preparation of entangled cat states, and prove that the overhead for distance-three fault tolerance is logarithmic in the cat state size. These results apply both to near-term experiments with a few qubits, and to the general study of the asymptotic resource requirements of syndrome measurement and state preparation.
With $a$ flag qubits, previous methods use $O(a)$ flag patterns to identify faults. In order to use the same flag qubits more efficiently, we show how to use nearly all $2^a$ possible flag patterns, by constructing maximal-length paths through the $a$-dimensional hypercube. |
| first_indexed | 2024-03-11T16:09:25Z |
| format | Article |
| id | doaj.art-906fe18d4c3a4e1f82309a088976ccb8 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-11T16:09:25Z |
| publishDate | 2023-10-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-906fe18d4c3a4e1f82309a088976ccb82023-10-24T16:37:26ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-10-017115410.22331/q-2023-10-24-115410.22331/q-2023-10-24-1154Fault-tolerant syndrome extraction and cat state preparation with fewer qubitsPrithviraj PrabhuBen W. ReichardtWe reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an exponential reduction in qubit overhead over the previous best protocol. For a weight-$w$ stabilizer, we demonstrate that stabilizer measurement tolerating one fault needs at most $\lceil \log_2 w \rceil + 1$ ancilla qubits. If qubits reset quickly, four ancillas suffice. We also study the preparation of entangled cat states, and prove that the overhead for distance-three fault tolerance is logarithmic in the cat state size. These results apply both to near-term experiments with a few qubits, and to the general study of the asymptotic resource requirements of syndrome measurement and state preparation. With $a$ flag qubits, previous methods use $O(a)$ flag patterns to identify faults. In order to use the same flag qubits more efficiently, we show how to use nearly all $2^a$ possible flag patterns, by constructing maximal-length paths through the $a$-dimensional hypercube.https://quantum-journal.org/papers/q-2023-10-24-1154/pdf/ |
| spellingShingle | Prithviraj Prabhu Ben W. Reichardt Fault-tolerant syndrome extraction and cat state preparation with fewer qubits Quantum |
| title | Fault-tolerant syndrome extraction and cat state preparation with fewer qubits |
| title_full | Fault-tolerant syndrome extraction and cat state preparation with fewer qubits |
| title_fullStr | Fault-tolerant syndrome extraction and cat state preparation with fewer qubits |
| title_full_unstemmed | Fault-tolerant syndrome extraction and cat state preparation with fewer qubits |
| title_short | Fault-tolerant syndrome extraction and cat state preparation with fewer qubits |
| title_sort | fault tolerant syndrome extraction and cat state preparation with fewer qubits |
| url | https://quantum-journal.org/papers/q-2023-10-24-1154/pdf/ |
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