[2023-03-31] Dr. Ming-Chien Hsu,Researcher, Hon-Hai Quantum Computing Center,"Quantum state tomography via non-convex Riemannian gradient descent"

• 2023-03-31
• 宋欣薏(職務代理)

Title: Quantum state tomography via non-convex Riemannian gradient descent
Date: 2023-03-31  14:20-15:30
Location: CSIE R103
Speaker: Dr. Ming-Chien Hsu(徐銘鍵),Researcher, Hon-Hai Quantum Computing Center

Hosted by: Prof. Yen-Huan Li
 

Abstract:

The recovery of an unknown density matrix of large size requires huge computational resources. State-of-the-art performance has recently been achieved with the Factored Gradient Descent (FGD) algorithm and its variants since they are able to mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite the theoretical guarantee of a linear convergence rate, convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number $\kappa$ of the ground truth state. Consequently, the total number of iterations needed to achieve the estimation error $\varepsilon$ can be as large as $O(\sqrt{\kappa}\ln(\frac{1}{\varepsilon}))$. In this work, we derive a quantum state tomography scheme that improves the dependence on $\kappa$ to the logarithmic scale. Thus, our algorithm can achieve the approximation error $\varepsilon$ in $O(\ln(\frac{1}{\kappa\varepsilon}))$ steps. The improvement comes from the application of 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 the numerical results.

Biography:

Dr. Hsu joined Hon-Hai Quantum Computing Center in 2020. Before moving to Hon-Hai to do quantum computing research, he was a post-doc at National Sun Yat-sen University and  National University of Singapore and focused on theoretical condensed matter physics and topological materials. He got his Ph.D. degree and master's degree in Physics Department, National Taiwan University. His bachelor's degree is from the Electrical Engineering Department at National Tsing Hua University.