Controlling Quantum Stability

Masanao Ozawa

Chunxiang Song, Yanan Liu, Daoyi Dong +1 more

Quantum state stabilization is a pivotal element in the realm of quantum control, forming the bedrock for various quantum tasks. To achieve the stabilization of a quantum state, it is imperative to formulate effective control channels (represented by control Hamiltonians) and devise the appropriate control signals. In this study, we introduce a novel approach, the selection of control Hamiltonians through Deep reinforcement learning (SCH-DRL), to address the challenge of control Hamiltonian selection in quantum control. Deep reinforcement learning (DRL) is employed to generate control signals corresponding to control Hamiltonians, and SCH-DRL utilizes these control signals to recognize a set of simple and efficient control Hamiltonians, depending on different target states. This approach not only provides a method for control Hamiltonian selection in quantum state stabilization but also unveils the untapped potential of DRL for a broad spectrum of applications in the field of quantum information. Through applications in two-qubit and three-qubit scenarios, we demonstrate how the SCH-DRL method adeptly selects the quantity of control Hamiltonians for achieving the desired stability of quantum states.

Xiaolei Li, Changyun Wen, Jian‐Ge Wang

In this paper, we consider the fixed-time stabilization control problem of quantum systems modeled by Schrödinger equations. Firstly, the Lyapunov-based fixed-time stability criterion is extended to finite-dimensional closed quantum systems in the form of coherence vectors. Then for a two-level quantum system with single control input, a non-smooth fractional-order control law is designed using the relative state distance. By integrating the fixed-time Lyapunov control technique and the bi-limit homogeneity theory, the quantum system is proved to be stabilized to an eigenstate of the inherent Hamiltonian in a fixed time. Comparing with existing methods in quantum system control, the proposed approach can guarantee stabilization in a fixed time without depending on the initial states.

Paola Cappallaro

XU Wen-bo

To the problem that,due to the unitary invariance of the Hilbert-space overlap of quantum states,classical stability concepts make little sense in the quantum dynamics,the linear response formalism of fidelity decay is employed to measure the stability of constructive control of quantum systems with respect to static perturbations.By analysing the fidelity decay of the constructive control of the quantum two-level systems,the stability of the control system is enhanced when more control pulses have radial coordinates equal to π/2.The simulation results of two different constructive control schemes show the theoretical predictions.The methodology can be applied to design more robust quantum control systems.

Board on Physics and Astronomy, Division on Engineering and Physical Sciences, National Academies of Sciences, Engineering, and Medicine