Rebing Wu

Protecting Coherence and Entanglement by Quantum Feedback Controls

When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.

Quantum feedback: Theory, experiments, and applications

The control of individual quantum systems is now a reality in a variety of physical settings. Feedback control is an important class of control methods because of its ability to reduce the effects of noise. In this review we give an introductory overview of the various ways in which feedback may be implemented in quantum systems, the theoretical methods that are currently used to treat it, the experiments in which it has been demonstrated to-date, and its applications. In the last few years there has been rapid experimental progress in the ability to realize quantum measurement and control of mesoscopic systems. We expect that the next few years will see further rapid advances in the precision and sophistication of feedback control protocols realized in the laboratory.

Characterization of the critical submanifolds in quantum ensemble control landscapes

The quantum control landscape is defined as the functional that maps the control variables to the expectation values of an observable over the ensemble of quantum systems. Analyzing the topology of such landscapes is important for understanding the origins of the increasing number of laboratory successes in the optimal control of quantum processes. This paper proposes a simple scheme to compute the characteristics of the critical topology of the quantum ensemble control landscapes showing that the set of disjoint critical submanifolds one-to-one corresponds to a finite number of contingency tables that solely depend on the degeneracy structure of the eigenvalues of the initial system density matrix and the observable whose expectation value is to be maximized. The landscape characteristics can be calculated as functions of the table entries, including the dimensions and the numbers of positive and negative eigenvalues of the Hessian quadratic form of each of the connected components of the critical submanifolds. Typical examples are given to illustrate the effectiveness of this method.

Control landscapes for observable preparation with open quantum systems

A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum dynamics phenomena. This paper extends the concept to encompass the broader context of the environment having an influence. For the case that the open system dynamics are fully controllable, it is shown that the control landscape for open systems can be lifted to the analysis of an equivalent auxiliary landscape of a closed composite system that contains the environmental interactions. This inherent connection can be analyzed to provide relevant information about the topology of the original open system landscape. Application to the optimization of an observable expectation value reveals the same landscape simplicity observed in former studies on closed systems. In particular, no false suboptimal traps exist in the system control landscape when seeking to optimize an observable, even in the presence of complex environments. Moreover, a quantitative study of the control landscape of a system interacting with a thermal environment shows that the enhanced controllability attainable with open dynamics significantly broadens the range of the achievable observable values over the control landscape.

Maximal suppression of decoherence in Markovian quantum systems

In this paper, we design an optimal control law to suppress decoherence effects in Markovian open quantum systems. The optimal control law is subject to the tracking precision of the trajectory governed by the free system, which is ideally free from decoherence. We observe from numerical simulation that the undesired decohering dynamics can be partially squeezed out in most systems. Moreover, we observe the existence of sinusoidally oscillating resonant modes that play dominant roles in the controlled trajectory, which can be easily realized by continuous wave pulses. These key features are strictly demonstrated in subsequent analysis under proper assumptions. For systems in which the coherent control does not work, we suggest a feedback control strategy to extend the applicability of control to wider class of systems.

Singularities of quantum control landscapes

A quantum control landscape is defined as the objective to be optimized as a function of the control variables. Existing empirical and theoretical studies reveal that most realistic quantum control landscapes are generally devoid of false traps. However, the impact of singular controls has yet to be investigated, which can arise due to a singularity on the mapping from the control to the final quantum state. We provide an explicit characterization of such controls that are strongly Hamiltonian-dependent and investigate their associated landscape geometry. Although in principle the singularities may correspond to local traps, we did not find any in numerical simulations. Also, as they occupy a small portion of the entire set of possible critical controls, their influence is expected to be much smaller than controls corresponding to the commonly located regular extremals. This observation supports the established ease of optimal searches to find high-quality controls in simulations and experiments.

Quantum Coherent Nonlinear Feedback With Applications to Quantum Optics on Chip

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.

Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations

Generating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many analytical and numerical studies have identified the minimum time necessary to implement a variety of quantum gates on coupled-spin qubit systems. This work focuses on exploring the Pareto front that quantifies the trade-off between the competitive objectives of maximizing the gate fidelity

Control landscapes for two-level open quantum systems

\mathcal{F}

Smooth controllability of infinite-dimensional quantum-mechanical systems

and minimizing the control time