Minimal entanglement for injecting diagonal gates
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929293582401536 |
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| author | Kliuchnikov, Vadym Schoute, Eddie |
| author_facet | Kliuchnikov, Vadym Schoute, Eddie |
| contents | Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then be consumed by a stabilizer circuit to implement non-Clifford operations. We show that the connectivity between the computational space and magic state factories forms a fundamental bottleneck on the rate at which non-Clifford operations can be implemented. We show that the nullity of the magic state, $ν(|D\rangle)$ for diagonal gate $D$, characterizes the non-local resources required to implement $D$ in the computational space. As part of our proof, we construct local stabilizer circuits that use only $ν(|D\rangle)$ ebits to implement $D$ in the computational space that may be useful to reduce the non-local resources required to inject non-Clifford gates. Another consequence is that the edge-disjoint path compilation algorithm [arXiv:2110.11493] produces minimum-depth circuits for implementing single-qubit diagonal gates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal entanglement for injecting diagonal gates Kliuchnikov, Vadym Schoute, Eddie Quantum Physics Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then be consumed by a stabilizer circuit to implement non-Clifford operations. We show that the connectivity between the computational space and magic state factories forms a fundamental bottleneck on the rate at which non-Clifford operations can be implemented. We show that the nullity of the magic state, $ν(|D\rangle)$ for diagonal gate $D$, characterizes the non-local resources required to implement $D$ in the computational space. As part of our proof, we construct local stabilizer circuits that use only $ν(|D\rangle)$ ebits to implement $D$ in the computational space that may be useful to reduce the non-local resources required to inject non-Clifford gates. Another consequence is that the edge-disjoint path compilation algorithm [arXiv:2110.11493] produces minimum-depth circuits for implementing single-qubit diagonal gates. |
| title | Minimal entanglement for injecting diagonal gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.18900 |