Limits of optimal control yields achievable with quantum controllers

In quantum optimal control theory, kinematic bounds are the minimum and maximum values of the control objective achievable for any physically realizable system dynamics. For a given initial state of the system, these bounds depend on the nature and state of the controller. We consider a general situation where the controlled quantum system is coupled to both an external classical field (referred to as a classical controller) and an auxiliary quantum system (referred to as a quantum controller). In this general situation, the kinematic bound is between the classical kinematic bound (CKB), corresponding to the case when only the classical controller is available, and the quantum kinematic bound (QKB), corresponding to the ultimate physical limit of the objectives value. Specifically, when the control objective is the expectation value of a quantum observable (a Hermitian operator on the systems Hilbert space), the QKBs are the minimum and maximum eigenvalues of this operator. We present, both qualitatively and quantitatively, the necessary and sufficient conditions for surpassing the CKB and reaching the QKB, through the use of a quantum controller. The general conditions are illustrated by examples in which the system and controller are initially in thermal states. The obtained results provide a basis for the design of quantum controllers capable of maximizing the control yield and reaching the ultimate physical limit.

Signal Flows in Non-Markovian Linear Quantum Feedback Networks

Enabled by rapidly developing quantum technologies, it is possible to network quantum systems at a much larger scale in the near future. To deal with non-Markovian dynamics that is prevalent in solid-state devices, we propose a general transfer function based framework for modeling linear quantum networks, in which signal flow graphs are applied to characterize the network topology by flow of quantum signals. We define a noncommutative ring $mathbb{D}$ and use its elements to construct Hamiltonians, transformations and transfer functions for both active and passive systems. The signal flow graph obtained for direct and indirect coherent quantum feedback systems clearly show the feedback loop via bidirectional signal flows. Importantly, the transfer function from input to output field is derived for non-Markovian quantum systems with colored inputs, from which the Markovian input-output relation can be easily obtained as a limiting case. Moreover, the transfer function possesses a symmetry structure that is analogous to the well-know scattering transformation in sd picture. Finally, we show that these transfer functions can be integrated to build complex feedback networks via interconnections, serial products and feedback, which may include either direct or indirect coherent feedback loops, and transfer functions between quantum signal nodes can be calculated by the Riegles matrix gain rule. The theory paves the way for modeling, analyzing and synthesizing non-Markovian linear quantum feedback networks in the frequency-domain.

Spectral Analysis and Identification of Noises in Quantum Systems

In quantum information processing, knowledge of the noise in the system is crucial for high-precision manipulation and tomography of coherent quantum operations. Existing strategies for identifying this noise require the use of additional quantum devices or control pulses. We present a noise-identification method directly based on the systems non-Markovian response of an ensemble measurement to the noise. The noise spectrum is identified by reversing the response relationship in the frequency domain. For illustration, the method is applied to superconducting charge qubits, but it is equally applicable to any type of qubits. We find that the identification strategy recovers the well-known Fermis golden rule under the lowest-order perturbation approximation, which corresponds to the Markovian limit when the measurement time is much longer than the noise correlation time. Beyond such approximation, it is possible to further improve the precision at the so-called optimal point by incorporating the transient response data in the non-Markovian regime. This method is verified with experimental data from coherent oscillations in a superconducting charge qubit.

The role of controllability in optimizing quantum dynamics

This paper discusses the important role of controllability played on the complexity of optimizing quantum mechanical control systems. The study is based on a topology analysis of the corresponding quantum control landscape, which is referred to as the optimization objective as a functional of control fields. We find that the degree of controllability is closely relevant with the ruggedness of the landscape, which determines the search efficiency for global optima. This effect is demonstrated via the gate fidelity control landscape of a system whose controllability is restricted on a SU(2) dynamic symmetry group. We show that multiple local false traps (i.e., non-global suboptima) exist even if the target gate is realizable and that the number of these traps is increased by the loss of controllability, while the controllable systems are always devoid of false traps.