近日，太原理工大学贺衎团队实现了用广义测量方法降低阴影处理层析成像的复杂性。相关论文于2025年7月14日发表在《物理评论A》杂志上。

量子过程断层扫描（QPT）对于推进量子技术至关重要，包括量子计算机、量子网络和量子传感器。阴影过程层析成像（SPT）利用Choi同构将QPT映射到阴影状态层析成像（SST），显著降低了从量子过程中提取信息的样本复杂度。然而，SPT依赖于随机的酉算子，使阴影范数最小的最优酉算子的确定变得复杂，而阴影范数是影响样本复杂度的关键因素。

研究组提出了一个广义的SPT框架，通过用广义测量（正算子值测量（POVM））代替酉算子来最小化阴影范数。这种方法被称为带有POVM的阴影过程断层扫描（POVM-SPT），其主题是凸优化，以确定最小化阴影范数的最佳POVM，从而进一步降低样本复杂性。

研究组通过数值模拟证明了最优POVM的识别，并提供了相应的优化算法。他们的数值实验表明，与传统的SPT相比，POVM-SPT实现了阴影范数的大幅降低，单量子位输入状态提高了大约7倍，64量子位输入状态提高了2180倍。这些结果表明，POVM-SPT在简化SPT任务方面具有显著优势，特别是对于大规模量子系统。

附：英文原文

Title: Reducing complexity of shadow process tomography with generalized measurements

Author: Haigang Wang, Kan He

Issue&Volume: 2025/07/14

Abstract: Quantum process tomography (QPT) is crucial for advancing quantum technologies, including quantum computers, quantum networks, and quantum sensors. Shadow process tomography (SPT) utilizes the Choi isomorphism to map QPT to shadow state tomography (SST), significantly reducing the sample complexity for extracting information from quantum processes. However, SPT relies on random unitary operators and complicates the determination of the optimal unitary operator that minimizes the shadow norm, which is the key factor influencing the sample complexity. In this work, we propose a generalized SPT framework that minimizes the shadow norm by replacing unitary operators with generalized measurements [positive operator-valued measures (POVMs)]. This approach, termed shadow process tomography with POVMs (POVM-SPT), uses convex optimization to identify the optimal POVM for minimizing the shadow norm, thereby further reducing sample complexity. We demonstrate the identification of the optimal POVM through numerical simulations and provide the corresponding optimization algorithms. Our numerical experiments demonstrate that POVM-SPT achieves a substantial reduction in the shadow norm compared to conventional SPT, with an approximate sevenfold improvement for single-qubit input states and a remarkable 2180-fold enhancement for 64-qubit input states. These results reveal that POVM-SPT offers significant advantages in simplifying SPT tasks, particularly for large-scale quantum systems.

DOI: 10.1103/13ct-8vtv

Source: https://journals.aps.org/pra/abstract/10.1103/13ct-8vtv