Francesco Tacchino (IBM Research, Zurich) — Informationally complete tools for quantum computation

Title: Informationally complete tools for quantum computation

Abstract:
Informationally complete (IC) measurements represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. In this talk, I will first review some adaptive protocols leveraging IC POVMs to reduce the sampling cost of operator averaging, and I will comment on their practical realisation on quantum processors. Following recent results in the literature, I will then connect these methods to the broader class of randomized measurement techniques, which notably include classical shadows, via the notion of measurement dual frames. These reveal the existence of additional degrees of freedom at the post-processing stage that are often neglected by established techniques. I will present novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies which significantly enhance the quality of statistical estimators constructed from IC samples while retaining full computational efficiency. Remarkably, these improvements come at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to any randomized measurement toolbox.

Date of talk: 2024-05-03