Abstract We present protocols for feedback control and stabilization of a single qubit undergoing Rabi oscillations. Using a hybrid quantum-classical Bayesian estimation technique we simulate monitoring of the dynamical parameter (Rabi frequency) of the governing Hamiltonian in real-time. We numerically demonstrate feedback control of the system parameter using a classical proportional-integral feedback control scheme and show that by implementing a unitary reversal of the back-action of the weak measurement the loop response time is dramatically reduced. This reversal is chosen by assuming the system is already executing the targeted dynamics, an approach called self-fulfilling prophecy . In addition, self-fulfilling prophecy reduces measurement induced noise, leading to stabilized dynamics.
Abstract We present protocols for feedback control and stabilization of a single qubit undergoing Rabi oscillations. Using a hybrid quantum-classical Bayesian estimation technique we simulate monitoring of the dynamical parameter (Rabi frequency) of the governing Hamiltonian in real-time. We numerically demonstrate feedback control of the system parameter using a classical proportional-integral feedback control scheme and show that by implementing a unitary reversal of the back-action of the weak measurement the loop response time is dramatically reduced. This reversal is chosen by assuming the system is already executing the targeted dynamics, an approach called self-fulfilling prophecy . In addition, self-fulfilling prophecy reduces measurement induced noise, leading to stabilized dynamics.
Fast measurement, signal processing, and accurate estimation of Hamiltonian parameters are essential for feedback control in quantum-classical interface circuitry. However, existing frequentist and Bayesian inference methods typically require a large number of measurements to achieve the accuracy needed to mitigate qubit decoherence. Consequently, feedback control of semiconductor qubits has largely been limited to single-qubit frequency stabilization, whereas two-qubit parameter stabilization remains experimentally unexplored. Here, we demonstrate a real-time feedback framework based on sequential Monte Carlo estimation using one bit of data from a single-shot measurement. Using a four-qubit semiconductor quantum dot device, we rapidly estimate individual qubit frequencies, yielding an approximately twofold increase in coherence time compared with a conventional Bayesian strategy. Moreover, sequential two-qubit parameter estimation using two bits of data enables stabilization of qubit-qubit coupling, allowing both quasi-static frequency drift and exchange-interaction noise to be estimated and suppressed. By shortening the time required for precise parameter estimation, these results demonstrate the importance of the synergistic development of classical and quantum electronics for building robust and scalable quantum technologies in fluctuating environments.
Measurement combined with feedback that aims to restore a presumed premeasurement quantum state will yield this state after a few measurement-feedback cycles even if the actual state of the system initially had no resemblance to the presumed state. Here we introduce this mechanism of self-fulfilling prophecy and show that it can be used to prepare finite-dimensional quantum systems in target states or force them into target dynamics. Using two-level systems as an example, we demonstrate that self-fulfilling prophecy protects the system against noise and tolerates imprecision of feedback up to the level of the measurement strength. By means of unsharp measurements the system can be driven deterministically into arbitrary, smooth quantum trajectories.
Abstract 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.
In this paper, we consider the real-time parameter estimation problem for a ZZ-coupled system composed of two qubits in the presence of spontaneous emission. To enhance the estimation precision of the coupling coefficient, we first propose two different control strategies, where the first one is feedback control based on quantum-jump detection, and the second one is hybrid control combining Markovian feedback and Hamiltonian control. The simulation results show that compared with free evolution, both control strategies can improve parameter precision and extend system coherence time. Then, on the basis of the two control strategies, we propose a practical single-parameter quantum recovery protocol, which includes the preparation of an optimal initial probe state, the active control and optimization of a system evolution process, the design of an adaptive measurement scheme, and the parameter estimation algorithm based on Bayesian estimation theory. In particular, by employing a batch-style adaptive measurement scheme, the parameter recovery is conducted and the effectiveness of the two control strategies is verified.
The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse time scale to be long compared to the feedback delay yields the best stabilization.
We discuss the operation of the one-qubit quantum feedback loop, which may be used for initialization of a qubit in a solid-state quantum computer. The continuous monitoring of a quantum state, which makes the feedback possible, is done by means of a weak continuous measurement and processing of the obtained information via quantum Bayesian equations. The properly designed quantum feedback loop can keep the desired phase of a single-qubit quantum coherent oscillations for infinitely long time, even in presence of a dephasing environment. Various nonidealities reduce the fidelity of the feedback synchronization. We report our study of the effects of finite available bandwidth and time delay on the one-qubit quantum feedback performance, and also discuss the effect of environment-induced dephasing.