标题： 梯度下降方法用于快速量子态层析成像 显示英文标题

标题： Gradient-descent methods for fast quantum state tomography

摘要： 量子态层析成像（QST）是一种广泛用于表征量子系统状态的技术。 然而，它面临着两个基本挑战：随着量子比特数量的增加，计算和实验复杂度呈指数增长，即使对于中等规模的系统，实验实施和数据后处理也变得困难。 在此，我们引入了用于离散和连续变量系统中QST后处理步骤的梯度下降（GD）算法。 为了在算法的每个迭代步骤中确保物理上有效的状态重构，我们使用了各种密度矩阵参数化方法：Cholesky分解、Stiefel流形和投影归一化。 这些参数化方法还具有额外的好处，即能够实现受控秩的假设，当存在关于系统的先验信息时，这可以简化重构过程。 我们将我们的GD-QST技术与最先进的方法进行了基准测试，包括约束凸优化、条件生成对抗网络和迭代最大似然估计。 我们的比较重点在于时间复杂度、迭代次数、数据需求、状态秩和对噪声的鲁棒性。 我们发现，在随机小批量GD-QST算法中的受控秩假设能够有效处理噪声和不完整数据集，其重构保真度显著高于其他方法。 在标准笔记本电脑上实现全秩七量子比特QST，仅需不到三分钟，配备18 GB内存且无专用GPU，表明GD-QST在计算上更高效，并在大多数情况下优于其他技术，为表征噪声中等规模量子设备提供了一条有前景的途径。 我们用于GD-QST算法的Python代码可在https://github.com/mstorresh/GD-QST公开获取。 显示英文摘要

摘要： Quantum state tomography (QST) is a widely employed technique for characterizing the state of a quantum system. However, it is plagued by two fundamental challenges: computational and experimental complexity grows exponentially with the number of qubits, rendering experimental implementation and data post-processing arduous even for moderately sized systems. Here, we introduce gradient-descent (GD) algorithms for the post-processing step of QST in discrete- and continuous-variable systems. To ensure physically valid state reconstruction at each iteration step of the algorithm, we use various density-matrix parameterizations: Cholesky decomposition, Stiefel manifold, and projective normalization. These parameterizations have the added benefit of enabling a rank-controlled ansatz, which simplifies reconstruction when there is prior information about the system. We benchmark the performance of our GD-QST techniques against state-of-the-art methods, including constrained convex optimization, conditional generative adversarial networks, and iterative maximum likelihood estimation. Our comparison focuses on time complexity, iteration counts, data requirements, state rank, and robustness against noise. We find that rank-controlled ansatzes in our stochastic mini-batch GD-QST algorithms effectively handle noisy and incomplete data sets, yielding significantly higher reconstruction fidelity than other methods. Simulations achieving full-rank seven-qubit QST in under three minutes on a standard laptop, with 18 GB of RAM and no dedicated GPU, highlight that GD-QST is computationally more efficient and outperforms other techniques in most scenarios, offering a promising avenue for characterizing noisy intermediate-scale quantum devices. Our Python code for GD-QST algorithms is publicly available at https://github.com/mstorresh/GD-QST.