Control Of Quantum Systems Based On Fixed-Time Stability And Quantum-Behaved Particle Swarm Optimization Algorithm

In recent years,quantum technology has attracted more and more attention as quantum computing,quantum communication and other fields continue to make break-throughs.The intensive research of quantum control problems plays a significant role in promoting the development of quantum science and technology.The fixed-time con-trol of quantum systems can shorten the time of state transfer and has better robust-ness,which can effectively reduce the influence of decoherence on the evolution of the system.At present.the fixed-time control problem of quantum systems and the high-fidelity transfer problem of high-dimensional complex quantum systems to any target pure state have not been well solved.In this context,this dissertation considers the con-trol problem of quantum systems based on fixed-time stability and quantum-behaved particle swarm optimization algorithm.The main research work could be summarized as follows.(1)A new continuous non-smooth control scheme is proposed to achieve fixed-time convergence to the target equilibrium state for the two-level quantum system de-scribed by the Liouville equation and meanwhile the robustness is analyzed.Firstly,the system model and the control target are equivalently transformed in terms of co-herence vectors and the exponential form of complex numbers,and then a continu-ous non-smooth control law with fractional powers is designed by a suitable Lyapunov function.Secondly,the bi-limit homogeneity approximation theory and the fixed-time Lyapunov stability theorem are used to obtain a sufficient condition that the controlled quantum system realizes fixed-time convergence.In particular,since certain values of the fractional powers in the control law cannot guarantee the accurate convergence of the quantum system,two non-smooth switching control strategies are proposed to improve control performances and then ensure complete convergence to the target equilibrium state within a fixed time.Furthermore,the impact of various uncertainties that may ex-ist in actual quantum manipulations on the fixed-time stability of the controlled system is analyzed.Finally,the effectiveness of the proposed scheme is verified by numerical simulation experiments.It is shown that the non-smooth control has better robustness than the standard Lyapunov control.(2)Based on the Lyapunov stability theory and the quantum-behaved particle swarm optimization algorithm,a new Lyapunov control scheme is proposed to drive finite-dimensional closed and Markovian open quantum systems into any desired target pure state with as high fidelity and as little time as possible.Firstly,the control laws are established by a Lyapunov function with a Hermitian operator to be constructed,and the eigenvectors of the operator are structured based on the condition that the LaSalle in-variant set contains the desired target state.Secondly,a set of optimal eigenvalues of the Hermitian operator is found by the quantum-behaved particle swarm optimization al-gorithm,and then the unknown operator is constructed.Particularly,since the designed control law may be very large when its denominator is quite small during the system evolution,an improved strategy with constraints is presented based on the quantum-behaved particle swarm optimization algorithm to enhance the flexibility of the control laws in implementation.Finally,numerical simulation experiments are carried out on a five-level closed quantum system,a four-qubit closed quantum system,a five-level open quantum system,and a ten-level open quantum system.The simulation results demonstrate that the proposed control scheme is a good solution to the rapid and high-fidelity transfer problem to any target state for high-dimensional quantum systems.