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Dispersive-dissipative control strategy for quantum coherent feedback

Yoshiki Kashiwamura, Naoki Yamamoto

Published Jul 1, 2017• 3 citations
Publisher

Abstract

To control a quantum system, recently the coherent feedback method has attracted wide attention thanks to its several advantages over the conventional measurement-based feedback method. However, for nonlinear quantum systems, no systematic guiding principle for designing a coherent feedback controller has been known, while for the measurement case one can employ the so-called quantum non-demolition (QND) feedback method as a systematic strategy. In this paper, we develop a coherent feedback counterpart of this QND-based control strategy. The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and single photon production.

DOI
10.1016/j.ifacol.2017.08.1984

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To control a quantum system, recently the coherent feedback method has attracted wide attention thanks to its several advantages over the conventional measurement-based feedback method. However, for nonlinear quantum systems, no systematic guiding principle for designing a coherent feedback controller has been known, while for the measurement case one can employ the so-called quantum non-demolition (QND) feedback method as a systematic strategy. In this paper, we develop a coherent feedback counterpart of this QND-based control strategy. The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and single photon production.
Measurement feedback is a versatile and powerful tool, although its performance is limited by several practical imperfections resulting from classical components. This paper shows that, for some typical quantum feedback control problems for state preparation (stabilization of a qubit or a qutrit, spin squeezing, and Fock state generation), the classical feedback operation can be replaced by a fully quantum one such that the state autonomously dissipates into the target or a state close to the target. The main common feature of the proposed quantum operation, which is called coherent feedback, is that it is composed of a series of dispersive and dissipative couplings inspired by the corresponding measurement feedback scheme.
This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.
In the control of classical mechanical systems, feedback has been applied to the generation of desired nonlinear dynamics, e.g., in chaos control. However, how much this can be done is still an open problem in quantum mechanical systems. This paper presents a scheme of enhancing nonlinear quantum effects via the recently developed coherent feedback techniques, which can be shown to outperform the measurement-based quantum feedback scheme that can only generate pseudo-nonlinear quantum effects. Apart from the advantages of our method, an unsolved problem is that the decoherence rate is also increased by the quantum amplifier, which may be solved by introducing, e.g., an integral device or an nonlinear quantum amplifier. Such a proposal is demonstrated via two application examples in quantum optics on chip. In the first example, we show that nonlinear Kerr effect can be generated and amplified to be comparable with the linear effect in a transmission line resonator (TLR). In the second example, we show that by tuning the gains of the quantum amplifiers in a TLR coherent feedback network, the resulting nonlinear effects can generate and manipulate non-Gaussian “light” (microwave field) which exhibits fully quantum sub-Poisson photoncount statistics and photon antibunching phenomenon. The scheme opens up broad applications in engineering nonlinear quantum optics on chip. Particularly, in this study, the concept of feedback nonlinearization which is very useful for quantum feedback control systems is introduced. This is in contrast to the feedback linearization concept used in classical nonlinear feedback control systems.
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the corresponding optimal principle. At last, we considered the exact decoherence dynamics of a qubit in a dissipative reservoir composed of harmonic oscillators, and demonstrated the effectiveness of our optimal control strategy. Simulation results showed that the coherence will completely lost in the absence of control neither in non-Markovian nor Markovian system. However, the optimal feedback control steers it to a stationary stochastic process which fluctuates around the target. In this case the decoherence can be controlled effectively, which indicates that the engineered artificial reservoirs with optimal feedback control may be designed to protect the quantum coherence in quantum information and quantum computation.
Sensitive measurement of the state of a qubit is crucial to the implementation of quantum information processing. This paper proposes a strategy to utilize a static bifurcation induced by nonlinear quantum feedback control to read out the state of a charge qubit that is dispersively coupled to a transmission line resonator. Compared with the traditional dispersive qubit readout strategy, the main advantage of our proposal is that even a weak qubit-resonator coupling is hopeful to lead to a strong measurement by varying the nonlinear feedback control parameter. This work opens up new perspectives for the applications of nonlinear quantum feedback control.