Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914848380551168 |
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| author | Butt, Friederike Heußen, Sascha Rispler, Manuel Müller, Markus |
| author_facet | Butt, Friederike Heußen, Sascha Rispler, Manuel Müller, Markus |
| contents | Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the T-gate missing in the two-dimensional and the H-gate in the three-dimensional case. These complementary shortcomings of the isolated topologies may be overcome in a combined approach, by switching between a two- and a three-dimensional code while maintaining the logical state. In this work, we construct resource-optimized deterministic and non-deterministic code switching protocols for two- and three-dimensional distance-three color codes using fault-tolerant quantum circuits based on flag-qubits. Deterministic protocols allow for the fault-tolerant implementation of logical gates on an encoded quantum state, while non-deterministic protocols may be used for the fault-tolerant preparation of magic states. Taking the error rates of state-of-the-art trapped-ion quantum processors as a reference, we find a logical failure probability of $3\%$ for deterministic logical gates, which cannot be realized transversally in the respective code. By replacing the three-dimensional distance-three color code in the protocol for magic state preparation with the morphed code introduced in [1], we reduce the logical failure rates by two orders of magnitude, thus rendering it a viable method for magic state preparation on near-term quantum processors. Our results demonstrate that code switching enables the fault-tolerant and deterministic implementation of a universal gate set under realistic conditions, and thereby provide a practical avenue to advance universal, fault-tolerant quantum computing and enable quantum algorithms on first, error-corrected logical qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17686 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors Butt, Friederike Heußen, Sascha Rispler, Manuel Müller, Markus Quantum Physics Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the T-gate missing in the two-dimensional and the H-gate in the three-dimensional case. These complementary shortcomings of the isolated topologies may be overcome in a combined approach, by switching between a two- and a three-dimensional code while maintaining the logical state. In this work, we construct resource-optimized deterministic and non-deterministic code switching protocols for two- and three-dimensional distance-three color codes using fault-tolerant quantum circuits based on flag-qubits. Deterministic protocols allow for the fault-tolerant implementation of logical gates on an encoded quantum state, while non-deterministic protocols may be used for the fault-tolerant preparation of magic states. Taking the error rates of state-of-the-art trapped-ion quantum processors as a reference, we find a logical failure probability of $3\%$ for deterministic logical gates, which cannot be realized transversally in the respective code. By replacing the three-dimensional distance-three color code in the protocol for magic state preparation with the morphed code introduced in [1], we reduce the logical failure rates by two orders of magnitude, thus rendering it a viable method for magic state preparation on near-term quantum processors. Our results demonstrate that code switching enables the fault-tolerant and deterministic implementation of a universal gate set under realistic conditions, and thereby provide a practical avenue to advance universal, fault-tolerant quantum computing and enable quantum algorithms on first, error-corrected logical qubits. |
| title | Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2306.17686 |