Measurement-induced Boolean dynamics and controllability for closed quantum networks
Qi, Hongsheng1,2; Mu, Biqiang1; Petersen, Ian R.3; Shi, Guodong4
Source PublicationAUTOMATICA
AbstractIn this paper, we study dynamical quantum networks which evolve according to Schrodinger equations but subject to sequential local or global quantum measurements. A network of qubits forms a composite quantum system whose state undergoes unitary evolution in between periodic measurements, leading to hybrid quantum dynamics with random jumps at discrete time instances along a continuous orbit. The measurements either act on the entire network of qubits, or only a subset of qubits. First of all, we reveal that this type of hybrid quantum dynamics induces probabilistic Boolean recursions representing the measurement outcomes. With global measurements, it is shown that such resulting Boolean recursions define Markov chains whose state-transitions are fully determined by the network Hamiltonian and the measurement observables. Particularly, we establish an explicit and algebraic representation of the underlying recursive random mapping driving such induced Markov chains. Next, with local measurements, the resulting probabilistic Boolean dynamics is shown to be no longer Markovian. The state transition probability at any given time becomes dependent on the entire history of the sample path, for which we establish a recursive way of computing such non-Markovian probability transitions. Finally, we adopt the classical bilinear control model for the continuous Schrodinger evolution, and show how the measurements affect the controllability of the quantum networks. (C) 2020 Elsevier Ltd. All rights reserved.
KeywordQuantum networks Quantum measurements Bilinear systems Boolean networks
Indexed BySCI
Funding ProjectNational Key R&D Program of China[2018YFA0703800] ; National Natural Science Foundation of China[61873262] ; National Natural Science Foundation of China[61733018] ; Australian Research Council[DP180101805] ; Australian Research Council[DP190103615]
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000519656500009
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Document Type期刊论文
Corresponding AuthorQi, Hongsheng
Affiliation1.Acad Math & Syst Sci, Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Australian Natl Univ, Res Sch Elect Energy & Mat Engn, Canberra, ACT 0200, Australia
4.Univ Sydney, Australian Ctr Field Robot, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW 2006, Australia
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GB/T 7714
Qi, Hongsheng,Mu, Biqiang,Petersen, Ian R.,et al. Measurement-induced Boolean dynamics and controllability for closed quantum networks[J]. AUTOMATICA,2020,114:11.
APA Qi, Hongsheng,Mu, Biqiang,Petersen, Ian R.,&Shi, Guodong.(2020).Measurement-induced Boolean dynamics and controllability for closed quantum networks.AUTOMATICA,114,11.
MLA Qi, Hongsheng,et al."Measurement-induced Boolean dynamics and controllability for closed quantum networks".AUTOMATICA 114(2020):11.
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