非克利福德量子纠错的多项式时间模拟

中文摘要 AI 辅助

我们证明，一类广泛的非克利福德量子纠错电路的每个中间态都是三阶相位多项式态，即使在随机泡利噪声下也是如此。该类电路包括魔法态蒸馏与培育、码切换与规范固定、带综合征提取的横向非克利福德门以及对角魔法态注入。三阶相位多项式态严格推广了稳定子态，我们证明它们恰好是我们引入的对角克利福德与泡利（DCP）稳定子形式体系中的稳定子态。我们刻画了这些态，并证明其表示可以在多项式时间内更新。这为这些电路提供了一种精确的多项式时间模拟算法，并且更广泛地，提供了一个用于推理其内部态及一般魔法态的框架。我们提供了开源实现\ exttt{merlin}，并在蒸馏、培育和码切换电路上将其与现有的非克利福德模拟器进行基准测试。基准测试表明，在Bravyi-Haah蒸馏中，随着逻辑输出数量的增加，运行时间和内存扩展性得到改善，并且能够模拟一个超出所有其他测试模拟器能力的码切换电路。

英文摘要

We show that every intermediate state of a broad class of non-Clifford quantum error-correction circuits is a third-order phase-polynomial state, even under stochastic Pauli noise. The class includes magic state distillation and cultivation, code switching and gauge fixing, transversal non-Clifford gates with syndrome extraction, and injection of diagonal magic states. Third-order phase-polynomial states strictly generalize stabilizer states, and we prove that they are exactly the stabilizer states of the diagonal-Clifford-and-Pauli (DCP) stabilizer formalism that we introduce. We characterize these states and show that their representations can be updated in polynomial time. This yields an exact polynomial-time simulation algorithm for these circuits and, more broadly, a framework for reasoning about their internal states and about magic states in general. We provide an open-source implementation, \texttt{merlin}, and benchmark it against existing non-Clifford simulators on distillation, cultivation, and code switching circuits. The benchmarks demonstrate improved runtime and memory scaling as the number of logical outputs grows in Bravyi-Haah distillation, and simulation of a code switching circuit beyond the reach of all other tested simulators.

发表机构

• University of Oxford（牛津大学）
• Freie Universität Berlin（柏林自由大学）

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