快速且确定的量子过程层析
Fast and Sure-ious Quantum Process Tomography
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中文总结 AI 辅助
本文证明部分归一化是量子信道Choi态的精确保真度投影，从而将量子态层析算法提升为量子过程层析算法，并给出保真度投影最小二乘法的样本复杂度与数值优势。
中文摘要 AI 辅助
量子过程层析（QPT）协议通常通过Choi-Jamiolkowski同构从量子态层析（QST）协议提升而来，代价是需要额外步骤来强制执行迹保持（TP）约束。现有方法分为两类。一类是民间部分归一化方法，它将密度估计夹在其输入边缘的逆平方根之间，具有闭式解，但仅作为启发式使用，其分析仅为渐近性的，且损失维度上的多项式因子。另一类是基于投影的方法，这些方法原理上合理，但没有闭式解，且随维度扩展性差。我们通过证明部分归一化是量子信道Choi态在保真度（等价于Bures距离或纯化距离）下的精确投影来解决这一二分法。因此，任何在保真度上具有保证的QST算法都可以通过一个保持Choi秩且以Kraus形式计算而无需对Choi维度进行特征分解的闭式共轭变换，提升为继承其样本复杂度的QPT算法。我们提升了两个单副本协议，并证明了非自适应协议（保真度投影最小二乘法）能以与1/ε成正比的信道使用次数恢复Choi秩并达到不保真度ε。数值上，对于低Choi秩的信道，它在精度上优于最先进的投影最小二乘法，并且在TP正则化步骤和返回估计的时间与内存上改善了数量级。
英文摘要
Quantum process tomography (QPT) protocols are often designed by lifting quantum state tomography (QST) protocols through the Choi-Jamiolkowski isomorphism, at the cost of an extra step enforcing the trace-preserving (TP) constraint. Existing approaches fall into two classes. The folklore partial normalization, which sandwiches the density estimate between inverse square roots of its input marginal, has a closed form but is used as a heuristic, its only analyses being asymptotic and losing a factor polynomial in the dimension. Projection-based methods are principled but have no closed forms and scale poorly with dimension. We resolve this dichotomy by showing that the partial normalization is the exact projection onto the Choi states of quantum channels in fidelity (equivalently in Bures or purified distance). Consequently, any QST algorithm with guarantees in fidelity lifts to a QPT algorithm that inherits its sample complexity, through a single closed-form congruence that preserves the Choi rank and is computed in Kraus form without any eigendecomposition of Choi dimension. We lift two single-copy protocols and prove that the non-adaptive one (Fidelity Projected Least Squares) recovers the Choi rank and reaches infidelity $\varepsilon$ from a number of channel uses proportional to $1/\varepsilon$. Numerically, for channels of low Choi rank, it improves on the state-of-the-art projected least squares in accuracy, and by orders of magnitude in the time and memory of the TP-regularization step and of the returned estimate.
发表机构
- Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
- Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。
