2019/04/04 by Hongsheng Qi, Biqiang Mu, Qi, Hongsheng +5
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #FOS: Electrical engineering #FOS: Physical sciences #Gene Regulatory Network Analysis #Molecular Communication and Nanonetworks #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1904.02366
openalex publication_date 2019/04/04 · openalex created_date 2019/04/11 · openalex updated_date 2026/07/28
In this paper, we study dynamical quantum networks which evolve according to Schrödinger 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 Schrödinger evolution, and show how the measurements affect the controllability of the quantum networks.