Measurement-Induced Boolean Dynamics from Open Quantum Networks⁎This research was supported in part by the National Key R&D Program of China under Grant 2018YFA0703800, the National Natural Science Foundation of China under Grants 61873262 and 61733018, and the Australian Research Council under Grants DP180101805 and DP190103615. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Qi, Hongsheng; Mu, Biqiang; Petersen, Ian R.; Shi, Guodong
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 275
• Page End: 280
• Publication Date: 2020
• Subjects: quantum networks -- open quantum systems -- quantum measurements -- Boolean networks; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.135
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper, we study the induced probabilistic Boolean dynamics for dynamical quantum networks subject to sequential quantum measurements. In this part of the paper, we focus on closed networks of quits whose states evolutions are described by a continuous Lindblad master equation. When measurements are performed sequentially along such continuous dynamics, the quantum network states undergo random jumps and the corresponding measurement outcomes can be described by a probabilistic Boolean network. First of all, we show that the state transition of the induced Boolean networks can be explicitly represented through realification of the master equation. Next, when the open quantum dynamics is relaxing in the sense that it possesses a unique equilibrium as a global attractor, structural properties including absorbing states, reducibility, and periodicity for the induced Boolean network are direct consequences of the relaxing property. Finally, we show that for quantum consensus networks as a type of non-relaxing open quantum network dynamics, the communication classes of the measurement-induced Boolean networks are encoded in the quantum Laplacian of the underlying interaction graph.