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Rapid Feedback Stabilization of Quantum Systems With Application to Preparation of Multiqubit Entangled States
- Source :
- IEEE Transactions on Cybernetics. 52:11213-11225
- Publication Year :
- 2022
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2022.
-
Abstract
- 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.
- Subjects :
- Lyapunov stability
Lyapunov function
Computer science
Degenerate energy levels
Observable
State (functional analysis)
Topology
Computer Science Applications
Human-Computer Interaction
symbols.namesake
Greenberger–Horne–Zeilinger state
Control and Systems Engineering
symbols
State space
Electrical and Electronic Engineering
W state
Software
Information Systems
Subjects
Details
- ISSN :
- 21682275 and 21682267
- Volume :
- 52
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Cybernetics
- Accession number :
- edsair.doi.dedup.....2db9e8bde91119bba2027a91e34d75ed