Error correction of quantum system dynamics via measurement-feedback control

In this paper, we generalize the application of a recently proposed quantum control technique called self-fulfilling prophesy (Uys et al 2018 Phys. Rev. A 97 060102) to achieve high-fidelity target quantum dynamics which are disturbed by unwanted external couplings, based on sequential unsharp measurements and tailored unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well-designed based on the eigenstates of the density matrices of the expected (without external couplings) dynamical states and their corresponding post-measurement states. By means of quantum state estimation, the mechanism of the measurement-feedback scheme is explained generally. For illustrative examples, we show that the dynamical trajectory errors caused by both constant couplings and time-varying couplings are substantially reduced in typical two-level and multi-level systems, i.e. the high-fidelity quantum dynamics are achieved. Furthermore, we discuss the influence of external coupling strength and measurement strength on system dynamics. Crucially, the scheme is universal and can be applied to any dimension systems. Thus, it may find applications in quantum information processing.