An efficient online estimation algorithm with measurement noise for time-varying quantum states

Abstract Inspired by the online alternating direction multiplier method (OADM), we propose an efficient online quantum state estimation (QSE) algorithm (QSE-OADM) for recovering time-varying quantum states in this paper. Specifically, in QSE-OADM, the density matrix recovery subproblem and measurement noise minimization subproblem are divided and solved separately without running the algorithm iteratively, which makes the proposed method much more efficient than all previous works. In the numerical experiments, for a 4-qubit system, the proposed algorithm can achieve more than 97.57% (fidelity) estimation accuracy after 71 samples, and the average runtime of per estimation is ( 4.19 ± 0.41 ) × 10 − 4 seconds, which reveals its superior performance comparing with existing online processing algorithms.