



01806nas a2200181   4500008004100000245007200041210006900113260001500182520123900197653002701436653003101463100002001494700001601514700001801530700001901548700002001567856003701587       2022                        eng d00aQuantum state tomography via non-convex Riemannian gradient descent0 aQuantum state tomography via nonconvex Riemannian gradient desce  c10/10/20223 a<p>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&minus;&minus;&radic;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.</p>10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aHsu, Ming-Chien1 aKuo, En-Jui1 aYu, Wei-Hsuan1 aCai, Jian-Feng1 aHsieh, Min-Hsiu  uhttps://arxiv.org/abs/2210.04717