Approximate bang-bang control assisted rapid switching feedback stabilization for stochastic qubit systems

For stochastic qubit systems under measurement feedback, an approximate bang-bang control assisted rapid switching control scheme with fewer switching times between the two subsets of state space is proposed in this paper. An eigenstate for single-qubit systems and any GHZ entangled state for multiqubit systems are prepared successfully. In our control scheme, the state space is partitioned into two parts: a subset S-1 containing the target state and its complementary set S-2. On each subset, a Lyapunov function is selected and the corresponding control law is designed, where the control laws in S-1 are of approximate bang-bang form and therefore can speed up the control process and the control laws in S-2 ensure the strictly monotonic descent of the corresponding Lyapunov function and therefore can reduce the switching times. In particular, for multi-qubit systems with degenerate measured observables, we use two control channels to distinguish the target state from other isospectral eigenstates. By properly constructing the control Hamiltonians and using stochastic Lyapunov stability theory, we prove that the switching control laws in this paper render the system trajectory to switch at most twice on the boundary of S-1 and S-2 and to converge to the target state contained in S-1 rapidly. Numerical simulations verify the effectiveness and rapidity of the proposed rapid control scheme. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a rapid switching control scheme for stochastic qubit systems under measurement feedback, aiming to reduce the switching times between the two subsets of the state space and improve the control efficiency. The scheme successfully prepares specific states for single-qubit and multiqubit systems. It utilizes approximate bang-bang control laws in subset S-1 to speed up the control process, and control laws in subset S-2 to ensure the descent of the corresponding Lyapunov function and reduce the switching times.