Quantum state tomography based on infidelity estimation

Quantum state tomography is a cornerstone of quantum information technologies to characterize and benchmark quantum systems from measurement statistics. In this work, we present an infidelity-based least-squares estimator, which incorporates the state purity information and provides orders of magnitude higher tomography accuracy than previous ones. It is further enhanced with the randomized toolbox of direct fidelity estimation, making it applicable to large-scale quantum systems. We validate the proposed estimators through extensive experiments conducted on the IBM Qiskit simulator. The results also demonstrate that our estimator admits an infidelity scaling with Pauli sample size N for (nearly) pure states. Further, it enables high-precision pure-state tomography for systems of up to 25-qubit states, given some state priors. Our method provides a novel perspective on the union of underlying tomography technique and state properties estimation.