Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 52, Issue 10, Pages 11213-11225Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2021.3090676
Keywords
Control systems; Switches; Quantum system; Lyapunov methods; Aerospace electronics; Feedback control; Quantum state; Entangled states; quantum systems; rapid feedback stabilization; stochastic Lyapunov stability; switching control
Categories
Funding
- National Natural Science Foundation of China [61873251, 61773370]
- National Natural Science Foundation of International (Regional) Cooperation and Exchanges Project [61720106009]
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This article proposes a rapid switching control scheme for stochastic quantum systems with measurement feedback, which can stabilize the eigenstate of an observable operator and achieve the preparation of entangled states in multiqubit systems. The strategy involves partitioning the state space and designing control laws to address convergence obstacles, leading to improved system trajectory and convergence speed.
For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a W state.\enlargethispage-8pt
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