Adaptive quantum state tomography with iterative particle filtering

Abstract

Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori knowledge of the experimentalists makes this family of methods an attractive choice for QST. However, specialized techniques for pure states do not work well for mixed states and vice versa. In this paper, we present an adaptive particle filter (PF) based QST protocol which improves the scaling of fidelity compared to nonadaptive Bayesian schemes for arbitrary multi-qubit states. This is due to the protocol's unabating perseverance to find the states's diagonal bases and more systematic handling of enduring problems in popular PF methods relating to the subjectivity of informative priors and the invalidity of particles produced by resamplers. Numerical examples and implementation on IBM quantum devices demonstrate improved performance for arbitrary quantum states and the application readiness of our proposed scheme.