Efficient Magic State Cultivation on $\mathbb{RP}^2$

• URL: http://arxiv.org/abs/2503.18657v1
• Date: Mon, 24 Mar 2025 13:20:57 GMT
• Title: Efficient Magic State Cultivation on $\mathbb{RP}^2$
• Authors: Zi-Han Chen, Ming-Cheng Chen, Chao-Yang Lu, Jian-Wei Pan,
• Abstract summary: We propose a new magic state cultivation protocol that produces a logical $mathrmT$ state on a rotated surface code.<n>Small $mathbbRP2$ codes are used to hold logical information and checked by syndrome extraction circuits.<n>Our 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.
• Score: 4.828791769306579
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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