Related papers: Time Optimal Quantum Control of Spinor States
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum…
The efficient generation of highly nonclassical quantum states is essential for emerging quantum technologies, yet it remains challenging due to decoherence and the long preparation times associated with conventional adiabatic protocols.…
A New theoretical formalism for the optimal quantum control has been presented. The approach stems from the consideration of describing the time-dependent quantum system in terms of the real physical observables, viz., the probability…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the…
Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
Finding minimal time and establishing the structure of the corresponding optimal controls which can transfer a given initial state of a quantum system into a given target state is a key problem of quantum control. In this work, this problem…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…
We show that combining ideas from the fields of quantum invariants and of optimal control can be used to design optimal quantum control solutions without explicit reference to quantum states. The states are specified only implicitly in…
This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity…
Quantum control of systems plays important roles in modern science and technology. The ultimate goal of quantum control is to achieve high fidelity universal control in the time-optimal way. Although high fidelity universal control has been…
We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived.…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian…