量子门集中小马尔可夫误差的规范不变理论
A gauge-invariant theory of small Markovian errors in quantum gate sets
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中文总结 AI 辅助
该研究针对量子门集缺乏良好规范不变参数化的问题，提出了门集中小马尔可夫误差的微扰规范不变参数化方法，构建了一阶规范不变性质的向量空间，可用于参数化无规范自由度的门集并提取近似规范不变的误差度量。
中文摘要 AI 辅助
对量子计算寄存器（如一个或多个量子比特）的噪声逻辑操作可由作用于表示该寄存器量子态的密度矩阵上的转移矩阵（又称CPTP映射或超算子）线性描述，这些操作共同构成门集。门集具有规范自由度，许多看似不同的门集实际预测相同的实验结果，门集的性质只有具备规范不变性才是可观测的（即具有物理相关性）。遗憾的是，目前尚无良好的门集规范不变参数化方法。我们介绍了次优方案：对门集中小马尔可夫误差的微扰规范不变参数化。我们构建了一阶规范不变（FOGI）性质的向量空间，展示了如何构建和理解FOGI性质、如何将其用作坐标来参数化无规范自由度的门集，以及如何提取近似规范不变的误差度量。
英文摘要
Noisy logic operations on a quantum computational register -- e.g., one or more qubits -- can be described by transfer matrices (a.k.a. CPTP maps or superoperators) that act linearly on the density matrix representing the register's quantum state. Collectively, these operations form a gate set. Gate sets have a gauge freedom; many gate sets that appear different actually predict the same experimental outcomes. A property of a gate set can be observable (and thus physically relevant) only if it is gauge-invariant. Unfortunately, no good gauge-invariant parameterizations of gate sets are known. We introduce the next best thing, a perturbative gauge-invariant parameterization of small Markovian errors in gate sets. We construct vector spaces of properties that are first-order gauge-invariant (FOGI). We show how to construct and understand FOGI properties, how to use them as coordinates to parameterize gate sets without gauge freedom, and how to extract approximately gauge-invariant error metrics.
