Related papers: Quantum Lyapunov Control Based on the Average Valu…
A quantum system whose internal Hamiltonian is not strongly regular or/and control Hamiltonians are not full connected, are thought to be in the degenerate cases. In this paper, convergence problems of the multi-control Hamiltonians closed…
The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two…
We present a detailed analysis of the convergence properties of Lyapunov control for finite-dimensional quantum systems based on the application of the LaSalle invariance principle and stability analysis from dynamical systems and control…
Quantum Lyapunov control was developed in order to transform a quantum system from arbitrary initial states to a target state. The idea is to find control fields that steer the Lyapunov function to zero as $t\rightarrow \infty$, meanwhile…
In the interaction picture, a sufficient and necessary condition that guarantees the convergence of closed quantum control system is proposed in this paper. Theoretical derivation and the proof show that it is possible to achieve the…
We present detailed analysis of the convergence properties and effectiveness of Lyapunov control design for bilinear Hamiltonian quantum systems based on the application of LaSalle's invariance principle and stability analysis from…
Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang-bang…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
Quantum Lyapunov control, an important class of quantum control methods, aims at generating converging dynamics guided by Lyapunov-based theoretical tools. However, unlike the case of classical systems, disturbance caused by quantum…
The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector…
In the design of complex quantum systems like ion traps for quantum computing, it is usually desired to stabilize a particular system state or make the system state track a desired trajectory. Several control theoretical approaches based on…
Quantum state engineering is a central task in Lyapunov-based quantum control. Given different initial states, better performance may be achieved if the control parameters, such as the Lyapunov function, are individually optimized for each…
A Lyapunov-based control design for natural trajectory-tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for…
In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure…
We present a switching control strategy based on Lyapunov control for arbitrary state transitions in open qubit systems. With coherent vector representation, we propose a switching control strategy, which can prevent the state of the qubit…
Different ways of modelling quantum control systems, formulating control problems and solving the resulting problems are considered and compared. In particular, we compare the performance of geometric and optimal control, as well as…
We study the application of a generalized form of the level set method used in classical physical contexts to quantum optimal control situations. The set of OCT equations needed to keep the expectation value of an observable constant is…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with…