Pure State Feedback Switching Control Based on the Online Estimated State for Stochastic Open Quantum Systems

For the n-qubit stochastic open quantum systems,based on the Lyapunov stability theorem and LaSalle’s invariant set principle,a pure state switching control based on on-line estimated state feedback(short for OQST-SFC)is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state.The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method,in which the Lyapunov function is the state distance of the system.The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state,and a Lyapunov-based control is used to make the state enter the convergence domain and then continue to converge to the target state.At the same time,the continuous weak measurement of quantum system and the quantum state tomography method based on the on-line alternating direction multiplier(QST-OADM)are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller.Then,the pure state feedback switching control method based on the on-line estimated state feedback is realized in an n-qubit stochastic open quantum system.The complete derivation process of n-qubit QST-OADM algorithm is given;Through strict theoretical proof and analysis,the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given.The proposed control method is applied to a 2-qubit stochastic open quantum system for numerical simulation experiments.Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed,and the performances of the state transition under the corresponding cases are analyzed.

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

DTHMM based delay modeling and prediction for networked control systems

In the forward channel of a networked control system （NCS）, by defining the network states as a hidden Markov chain and quantizing the network-induced delays to a discrete sequence distributing over a finite time interval, the relation between the network states and the network-induced delays is modelled as a discrete-time hidden Markov model （DTHMM）. The expectation maximization （EM） algorithm is introduced to derive the maximumlikelihood estimation （MLE） of the parameters of the DTHMM. Based on the derived DTHMM, the Viterbi algorithm is introduced to predict the controller-to-actuator （C-A） delay during the current sampling period. The simulation experiments demonstrate the effectiveness of the modelling and predicting methods proposed.

Manipulations Between Eigenstates of 2-Level Quantum System Based on Optimal Measurements

This paper explores the manipulation between eigenstates in a two-level system by a sequence of instantaneous projective measurements. Three cases of the manipulations are studied: the manipulation of optimal measurement-based control; the optimal measurement-based manipulation with the effect of free evolution of system; and the external control fields being used to compensate for the effect caused by the free evolution. Numerical simulations are conducted to verify the results obtained from the theoretically analytical solutions. The optimal parameters for each manipulation case are obtained. The experimental results indicate that the external control fields can make the optimal measurement-based control more effective. © 2014 Chinese Association of Automation.

Generalized control of quantum systems in the frame of vector treatment

For the state control problem in finite-dimensional quantum systems with any initial state and a goal eigenstate, this paper studies the design method of control laws via the Lyapunov technology and in the vector frame, which ensures the convergence of any initial state toward the goal state. The stability of the closed-loop system in the goal eigenstate is analyzed and proven via the invariance principle. The simulation experiment on a spin-1/2 system shows the effectiveness of the designed control laws.

Comparison of time optimal control for two level quantum systems

The time optimal problem for a two level quantum sys-tem is studied. We compare two different control strategies of bang-bang control and the geometric control, respectively, es-pecial y in the case of minimizing the time of steering the state from North Pole to South Pole on the Bloch sphere with bounded control. The time performances are compared for different param-eters by the individual numerical simulation experiments, and the experimental results are analyzed. The results show that the ge-ometric control spends less time than the bang-bang control does.

Quantum gate-assisted teleportation in noisy environments:robustness and fidelity improvement

Quantum teleportation as the key strategy for quantum communication requires pure maximally shared entangled states among quantum nodes.In practice,quantum decoherence drastically degrades the shared entanglement during entanglement distribution,which is a serious challenge for the development of quantum networks.However,most of the decoherence control strategies proposed thus far are either resource-intensive or time-consuming.To overcome this obstacle,we enable noise-resistant teleportation through a noisy channel with a limited number of qubits and without applying time-consuming weak measurements.We apply a quantum gate control unit consisting of a controlled NOT gate and a rotation gate after the original teleportation protocol is accomplished.Furthermore,we demonstrate that a teleportation fidelity of unity is attainable when environment-assisted measurement is added to the proposed teleportation protocol via quantum gates.Moreover,we present an entanglement distribution process by employing the designed quantum gate control unit followed by the deterministic standard teleportation protocol to improve teleportation fidelity by establishing improved shared entanglement.Our performance analysis indicates that the proposed teleportation schemes offer a competitive fidelity and success probability compared with the conventional schemes and a recent weak measurement-based teleportation protocol.

Trajectory tracking control of quantum systems

For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems,with the help of concept in quantum system control,one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state.Therefore,the quantum state trajectory tracking problem becomes a steering one.State steering control law of the system transformed is designed by means of the Lyapunov stability theorem.Finally,numerical simulation experiments are given for a five-level energy quantum system.The comparison analysis of original system's trajectory tracking with other method illustrates the advantage in control time of the method proposed.

Feedback stabilization of N-dimensional stochastic quantum systems based on bang-bang control

For an N-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate measurement operator, respectively. In the switching control strategy, we divide the state space into two parts： a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate measurement operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous measurement theory; while for the case of a degenerate measurement operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate measurement operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.

State of the art and prospects of structured sensing matrices in compressed sensing

Compressed sensing （CS） enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampiing rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared.

PREPARATION OF ENTANGLEMENT STATES IN A TWO-SPIN SYSTEM BY LYAPUNOV-BASED METHOD

A stable Lyapunov-based control law is proposed for entanglement states preparation in this paper. Tbe mathematical model of a two-spin system is constructed in interaction picture. An average value of observable operator is selected as the Lyapunov fllnction. This paper designs the observable operator to make sure that the target state is stable in Lyapunov sense. Then the authors analyze the convergence of the control system, and demonstrate that the Bell states are asymptotically stable under the control law designed. Compared with other methods, the control method proposed in this paper has the advantages of easy design and convergence to the target states. Numerical simulation experiments for the preparation of Bell states are implemented.

State transfer based on decoherence-free target state by Lyapunov-based control

We propose a Lyapunov-based control approach for state transfer based on the decoherence-free target state. The expected target state is constructed to be a decoherence-free state in a decoherence-free subspace （DFS） by an external laser field I, so that the system state can be decoupled from the environment, and no more decoherence process will occur. With the decoherence-free target state, we design a Lyapunov-based control field II to steer the given initial state to the decoherence-free state of open quantum systems as completely as possible, and decouple the system state from the environment at the same time. In the end, it is verified that the state transfer control designed comes true on a A-type four-level atomic system, and the system can stay on the decoherence-free target state without coupling to environment.