利用两组互补投影测量的高效量子态层析
Efficient quantum state tomography with two complementary projective measurements
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中文总结 AI 辅助
本文提出一种基于Kirkwood-Dirac拟概率的量子态层析协议，仅需两组互补投影测量，结合复数逻辑回归与投影梯度算法，在GPU上20分钟内完成15量子比特混合态重构，显著降低测量与计算成本。
中文摘要 AI 辅助
量子态层析（QST）在量子信息处理中对于表征量子系统具有根本重要性，但其实际应用受到测量和计算成本指数增长的严重阻碍。本文提出了一种新颖的QST协议，利用Kirkwood-Dirac（KD）拟概率来重构量子态。首先，该协议仅需两组互补的秩一投影测量即可实现态重构，从而显著降低测量成本。其次，提出了一种复数逻辑回归估计器来处理收集到的KD数据，并辅以投影梯度算法以减轻数值不稳定性并加速收敛。进一步利用KD拟概率的乘积算子结构来降低计算成本。最后，进行了大量实验以验证我们协议的有效性。值得注意的是，在GPU实现下，随机生成的15量子比特混合态实例的完整重构可在20分钟内完成。这些结果表明了迈向可扩展QST及大规模量子系统基准测试的一条有前景的途径。
英文摘要
Quantum state tomography (QST) is of fundamental importance to characterize quantum systems in quantum information processing, but its practical implementation is severely hindered by the exponential scaling of measurement and computational costs. In this paper, we present a novel QST protocol that utilizes Kirkwood-Dirac (KD) quasiprobability to reconstruct quantum states. First, it enables state reconstruction with only two complementary rank-one projective measurements, thus significantly reducing the measurement cost. Then, a complex logistic regression estimator is proposed to process collected KD data, together with a projected gradient algorithm to mitigate numerical instability and to accelerate convergence. The product-operator structure of KD quasiprobability is further exploited to reduce the computational cost. Finally, extensive experiments are implemented to confirm the validity of our protocol. Notably, the full reconstruction of randomly generated 15-qubit mixed-state instances can be accomplished within 20 minutes under the GPU implementation. These results suggest a promising route toward scalable QST and benchmarking large-scale quantum systems.
