Improving Quantum state tomography via non-convex Riemannian gradient descent
Title: Improving Quantum state tomography via non-convex Riemannian gradient descent
Time: 14:10-15:10, January 12 (Thursday), 2023
Venue: Hybrid
Physical: PH5008, NSYSU
Online link: https://join.skype.com/q8a01iInPoBr
Abstract:
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(κ√ln(1ε)) 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(1κε)) 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.
reference: [arXiv:2210.04717] Quantum state tomography via non-convex Riemannian gradient descent
reference: [arXiv:2210.04717] Quantum state tomography via non-convex Riemannian gradient descent
