Oral: The Stabilized Analytic Continuation and the Randomized Measurement Toolbox

We develop a framework that can determine non-integer moments of density matrices via analytically continuing from the integer moments obtained using the randomized measurement toolbox. We compare our analytic continuation technique with the existing continuation schemes employed in the literature [1,2]. We establish the robustness of our protocol in terms of best estimation of the Von Neumann entropy over a large class of density matrices and against noisy input data. As a proof-of-principle experiment, we implement our protocol on the dataset from a trapped ion quantum computer [3]. We also discuss the adaptability of our protocol in more sophisticated scenarios, such as the measurements of Petz and sandwiched Renyi mutual informations.

[1] D’ Hoker et al, JHEP 2021(1), 1

[2] B. Vermersch et al, PRX Quantum, 5(1), 010352

[3] T Brydges et al, Science 364(6437), 260