Robust controllability of two-qubit Hamiltonian dynamics

Abstract

Physically, quantum gates (unitary gates) for quantum computation are implemented by controlling the Hamiltonian dynamics of quantum systems. When full descriptions of the Hamiltonians are given, the set of implementable quantum gates is easily characterized by quantum control theory. In many real systems, however, the Hamiltonians may include unknown parameters due to the difficulty of performing precise measurements or instability of the system. In this paper, we consider the situation that some parameters of the Hamiltonian are unknown, but we still want to perform a robust control of the Hamiltonian dynamics to implement a quantum gate irrespectively to the unknown parameters. The existence of the robust control was previously shown for single-qubit systems, and a constructive method was developed for two-qubit systems if a full control of each qubit is available. We analytically investigate the robust controllability of two-qubit systems, and apply Lie-algebraic approaches to handle the cases where only one of the two qubits is controllable. We also numerically analyze the robust controllability of the two-qubit systems where the analytical approach is not necessarily applicable and investigate the relationship between the robust controllability of systems with a discrete and continuous unknown parameter.

Robust quantum control with disorder-dressed evolution

“…Under realistic experimental conditions, we must expect that imprecise device control and uncontrolled external influences, e.g., stray fields, limit the accurate implementation of control pulses, resulting in deviations from the desired dynamics. Robust quantum control aims to mitigate the impact of such noise and disorder by identifying control pulses that uphold their performance even under the presence of perturbations, see, e.g., [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Robust control thus relies on the insight that control pulses are not unique, which gives us the freedom to further select them for robustness.…”

Optimal Probabilistic Quantum Control Theory

“…For the design of control strategy and methods, optimal control theory [20,21], Lyapunov control approaches [22][23][24], learning control algorithms [25] and robust control methods [26][27][28][29][30] have been developed for the manipulation of quantum systems and the achievement of various control objectives. Among the aforementioned control design approaches, quantum optimal control is recognized as a powerful method for many complex quantum control tasks and has been successfully implemented for finding a control strategy for controlling molecules.…”

Robustness of continuous non‐smooth finite‐time Lyapunov control for two‐level quantum systems

“…Ensemble control is another class of quantum robust control since different values of ensemble parameters characterising the system dynamics can be viewed as uncertainties. At present, the controllability of quantum ensembles has been analysed, e.g., for two‐level ensembles by the method of polynomial approximations in [23] and the study of the algebra of polynomials defined by non‐commuting vector fields in [24], and for two‐qubit ensembles via the polynomial approximation method and a discretisation method in [25]. It should be addressed that the controllability analysis implies the existence of robust control pulses and generally does not provide their construction.…”