发表机构
Faculty of Electronics and Telecommunications, University of Science, Vietnam National University Ho Chi Minh City (VNU-HCM); Identity Quantum Computing JSC（越南国家大学胡志明市科学大学电子与电信学院; Identity量子计算股份公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究比较变分量子电路中零温振幅阻尼与其无限温泡利twirl，隔离零温偏置对特征尺度的影响，发现可训练输出尺度可消除精度差异但增加测量采样成本，并指出阻尼方向在特定条件下为规范。
AI 中文摘要
振幅阻尼（AD）的泡利twirl是无限温度下的广义振幅阻尼：它保留了AD的收缩性，但去除了其非幺正项，因此在变分电路中比较两者可以隔离零温偏置，该偏置主要通过特征尺度起作用。对于随机参数，AD下的特征会落在一个底板上，在强阻尼下该底板由最后一层决定，具有闭式形式，且在固定$T_1$下随温度按$\tanh(\hbar\omega/2k_BT)$下降；在twirl下，特征每层按常数因子收缩，最多可达八比特。可训练的输出尺度消除了大部分由此产生的精度差异，在我们的模拟中，AD最多比其twirl高出约三个百分点；被消除的差异以测量射击成本的形式重新出现：以每幅图像$10^3$次射击进行训练和测试，在$p=0.3$下，四比特分类器在AD下的精度保持在无噪声精度的1.5个百分点以内，而twirled分类器损失高达33。在较弱阻尼下，分离深度大致按$(np)^{-1}\ln(1/p)$增长。当阻尼跟随完全纠缠层且电路边界可训练时，阻尼方向是一个规范；在特征值求解器中，它在分解的两比特门内变得物理化。
英文摘要
The Pauli twirl of amplitude damping (AD) is generalized amplitude damping at infinite temperature: it keeps the contraction of AD and removes its non-unital term, so comparing the two in variational circuits isolates the zero-temperature bias, which acts mainly through the scale of the features. For random parameters, features under AD settle on a floor, which at strong damping is set by the last layer, has a closed form, and at fixed $T_1$ falls with temperature as $\tanh(\hbarω/2k_BT)$; under the twirls they shrink by a constant factor per layer, up to eight qubits. A trainable output scale removes most of the resulting accuracy differences, leaving AD ahead of its twirls by at most about three percentage points in our simulations; what it removes reappears as a cost in measurement shots: trained and tested with $10^3$ shots per image, a four-qubit classifier under AD at $p=0.3$ stays within 1.5 points of noiseless accuracy, while the twirled classifiers lose up to 33. At weaker damping the separation depth grows roughly as $(np)^{-1}\ln(1/p)$. The damping direction is a gauge when the damping follows complete entangling layers and the circuit boundaries are trainable; in an eigensolver it becomes physical inside a decomposed two-qubit gate.
