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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2503.18657 |
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| _version_ | 1866909550166147072 |
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| author | Chen, Zi-Han Chen, Ming-Cheng Lu, Chao-Yang Pan, Jian-Wei |
| author_facet | Chen, Zi-Han Chen, Ming-Cheng Lu, Chao-Yang Pan, Jian-Wei |
| contents | Preparing high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among prior attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC), a recently proposed protocol for preparing $\mathrm{T}$ states without magic state distillation, achieves state-of-the-art efficiency. Inspired by this work, we propose a new MSC procedure that would produce a logical $\mathrm{T}$ state on a rotated surface code at a further reduced cost. For our MSC protocol, we define a new code family, the $\mathbb {RP}^2$ code, by putting the rotated surface code on $\mathbb{RP}^2$ (a two-dimensional manifold), as well as two self-dual CSS codes named SRP-3 and SRP-5 respectively. Small $\mathbb{RP}^2$ codes are used to hold logical information and checked by syndrome extraction (SE) circuits. We design fast morphing circuits that enable switching between a distance 3 (5) $\mathbb{RP}^2$ code and an SRP-3 (SRP-5) code on which we can efficiently check the correctness of the logical state. To preserve the high accuracy of the cultivated logical $\mathrm{T}$ state, we design an efficient and easy-to-decode expansion stage that grows a small $\mathbb{RP}^2$ code to a large rotated surface code in one round. Our MSC protocol utilizes non-local connectivity, available on both neutral atom array and ion trap platforms. According to our Monte Carlo sampling results, our MSC protocol requires about an order of magnitude smaller space-time volume to reach a target logical error rate around $10^{-9}$ compared to the original MSC protocol. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Magic State Cultivation on $\mathbb{RP}^2$ Chen, Zi-Han Chen, Ming-Cheng Lu, Chao-Yang Pan, Jian-Wei Quantum Physics Preparing high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among prior attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC), a recently proposed protocol for preparing $\mathrm{T}$ states without magic state distillation, achieves state-of-the-art efficiency. Inspired by this work, we propose a new MSC procedure that would produce a logical $\mathrm{T}$ state on a rotated surface code at a further reduced cost. For our MSC protocol, we define a new code family, the $\mathbb {RP}^2$ code, by putting the rotated surface code on $\mathbb{RP}^2$ (a two-dimensional manifold), as well as two self-dual CSS codes named SRP-3 and SRP-5 respectively. Small $\mathbb{RP}^2$ codes are used to hold logical information and checked by syndrome extraction (SE) circuits. We design fast morphing circuits that enable switching between a distance 3 (5) $\mathbb{RP}^2$ code and an SRP-3 (SRP-5) code on which we can efficiently check the correctness of the logical state. To preserve the high accuracy of the cultivated logical $\mathrm{T}$ state, we design an efficient and easy-to-decode expansion stage that grows a small $\mathbb{RP}^2$ code to a large rotated surface code in one round. Our MSC protocol utilizes non-local connectivity, available on both neutral atom array and ion trap platforms. According to our Monte Carlo sampling results, our MSC protocol requires about an order of magnitude smaller space-time volume to reach a target logical error rate around $10^{-9}$ compared to the original MSC protocol. |
| title | Efficient Magic State Cultivation on $\mathbb{RP}^2$ |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.18657 |