Fast Quantum Process Tomography via Riemannian Gradient Descent
This work addresses the challenge of constrained optimization in quantum physics and information science, offering a faster and accurate method for characterizing quantum processes, which is incremental as it builds on existing Riemannian optimization techniques.
The paper tackles the problem of quantum process tomography, which aims to reconstruct quantum processes from measurement data, by introducing a modified stochastic gradient descent method on Riemannian manifolds, achieving order-of-magnitude faster results with accurate performance compared to traditional approaches like maximum likelihood estimation and projected least squares.
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.