Related papers: Discrete Adjoints for Accurate Numerical Optimizat…
We consider the optimal control problem of determining electromagnetic pulses for implementing logical gates in a closed quantum system, where the Hamiltonian models the dynamics of coupled superconducting qudits. The quantum state is…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
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…
We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…
In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of freedom irrelevant to physical observables) of the Schrodinger…
We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less…
In this work we introduce a new optimal control algorithm for the Keller-Segel chemo-attraction system, where both boundary and distributed controls are considered and both are associated with introducing/removing the amount of chemical…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…