单发态制备阈值：严格定理与统计力学映射
Single-shot state preparation threshold: rigorous theorem and statistical mechanical mapping
- Tsinghua University（清华大学）
- Frontier Science Center for Quantum Information（量子信息前沿科学中心）
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
- Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
- Hefei National Laboratory（合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明线性约束足以保证CSS量子LDPC码的单发态制备阈值，并通过统计力学映射和蒙特卡罗模拟表明亚线性健全性也可能支持该阈值。
AI中文摘要：
通过单轮噪声综合征测量制备逻辑码字可以减少容错量子计算的时间开销。目前尚不清楚码的哪些结构性质足以保证单发态制备的阈值。在此，我们证明对于CSS量子低密度奇偶校验码，线性约束足以保证非零的单发态制备阈值，这与通常认为健全性是必要的观点相反。当距离至少为对数级时，我们证明在非零局部随机读出和数据错误阈值以下，经过形式上的理想最终恢复后的逻辑错误概率呈指数级小，并且当码大小趋于无穷时趋近于零。在更强的线性健全性假设下，我们表明制备协议的残余数据错误是局部随机的，这直接允许与其他容错组件组合。为了研究超出上述假设的单发态制备阈值，我们进一步开发了一种统计力学映射，将最终逻辑错误率表示为经典配分函数。我们对三维环面码的该模型进行了蒙特卡罗模拟。数值结果表明，亚线性健全性也可以支持单发态制备阈值。
英文摘要：
Preparing logical codewords with a single round of noisy syndrome measurements can reduce the time overhead of fault-tolerant quantum computation. It remains unclear which structural properties of the code suffice to guarantee a threshold for single-shot state preparation. Here we prove that linear confinement suffices for a nonzero single-shot state-preparation threshold for CSS quantum low-density parity-check codes, in contrast to the common belief that soundness is necessary. When the distance is at least logarithmic, we prove that below nonzero local stochastic readout and data error thresholds, the logical error probability after a formal ideal final recovery is exponentially small and approaches zero when the code size approaches infinity. Under the stronger assumption of linear soundness, we show that the residual data error of the preparation protocol is local stochastic, directly allowing composition with other fault-tolerant gadgets. To investigate single-shot state-preparation threshold beyond the above assumptions, we further develop a statistical mechanical mapping that expresses the final logical error rate in terms of a classical partition function. We perform Monte Carlo simulations of this model for the three-dimensional toric code. The numerical results suggest that sublinear soundness can also support a single-shot state-preparation threshold.
