Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers.

翻译：约束优化在量子物理和量子信息科学领域发挥着关键作用，尤其对于高维复杂结构问题极具挑战性。一个具体问题便是量子过程层析成像，其目标是根据给定的测量数据集恢复底层量子过程。本文引入一种黎曼流形上的随机梯度下降改进版本，该版本整合了黎曼优化数值方法的最新进展。该方法天然支持量子过程的物理驱动约束，利用了最先进的大规模随机目标优化技术，且性能优于最大似然估计和投影最小二乘等传统方法。这种数据驱动方法不仅能实现准确且数量级更快的计算结果，还能处理不完整数据。我们通过量子过程仿真以及表征量子计算机上工程化过程的硬件实验，展示了该方法的有效性。