Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
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arXiv
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| Format: | Preprint |
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2024
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| author | Ouyang, Yingkai Jing, Yumang Brennen, Gavin K. |
| author_facet | Ouyang, Yingkai Jing, Yumang Brennen, Gavin K. |
| contents | Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem. Existing solutions like gate teleportation and magic state distillation are resource-intensive. We present a measurement-free code-switching protocol for universal quantum computation, switching between a stabiliser code for transversal Cliffords and a permutation-invariant (PI) code for transversal non-Cliffords that are logical $Z$ rotations for any rational multiple of $π$. The novel non-Clifford gates enabled by this code-switching protocol provide for a lower gate count implementation of a universal gate set relative to the Clifford$+T$ gate set. To achieve this, we present a protocol for performing controlled-NOTs between the codes using near-term quantum control operations that employ a catalytic bosonic mode. We also present a new class of PI codes with tunable code distance, supporting transversal non-Clifford gates, and demonstrate their reduced gate count overhead relative to a comparable stabilizer code to stabilizer code switching scheme. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_13142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measurement-free code-switching for low overhead quantum computation using permutation invariant codes Ouyang, Yingkai Jing, Yumang Brennen, Gavin K. Quantum Physics Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem. Existing solutions like gate teleportation and magic state distillation are resource-intensive. We present a measurement-free code-switching protocol for universal quantum computation, switching between a stabiliser code for transversal Cliffords and a permutation-invariant (PI) code for transversal non-Cliffords that are logical $Z$ rotations for any rational multiple of $π$. The novel non-Clifford gates enabled by this code-switching protocol provide for a lower gate count implementation of a universal gate set relative to the Clifford$+T$ gate set. To achieve this, we present a protocol for performing controlled-NOTs between the codes using near-term quantum control operations that employ a catalytic bosonic mode. We also present a new class of PI codes with tunable code distance, supporting transversal non-Clifford gates, and demonstrate their reduced gate count overhead relative to a comparable stabilizer code to stabilizer code switching scheme. |
| title | Measurement-free code-switching for low overhead quantum computation using permutation invariant codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.13142 |