2022/10/10 by Ming-Chien Hsu, Hsu, Ming-Chien, En-Jui Kuo +7 · 4 citations
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2210.04717
openalex publication_date 2022/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number κ of the ground truth state. Consequently, the total number of iterations can be as large as O(√κln((1)/(ε))) to achieve the estimation error ε. In this work, we derive a quantum state tomography scheme that improves the dependence on κ to the logarithmic scale; namely, our algorithm could achieve the approximation error ε in O(ln((1)/(κε))) steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results.