Related papers: Spectral Methods for Quantum Optimal Control: Arti…
The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum…
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…
Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
We address the generic problem of optimal quantum state preparation for open quantum systems. It is well known that open quantum systems can be simulated by quantum trajectories described by a stochastic Schr\"odinger equation. In this…
Reliable high-fidelity quantum state transformation has always been considered as an inseparable part of quantum information processing. In this regard, Pontryagin maximum principle has proved to play an important role to achieve the…
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…
We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for…
Complicated boundary conditions are essential to accurately describe phenomena arising in nature and engineering. Recently, the investigation of a potential speedup through quantum algorithms in simulating the governing ordinary and partial…
In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…
The formulation of the eigenvalue problem for the Schr\"odinger equation is studied, for the numerical solution a new approach is applied. With the usual exponentially rising free-state asymptotical behavior, and also with a first order…
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a…
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 represents a powerful technique to enhance the performance of quantum experiments by engineering the controllable parameters of the Hamiltonian. However, the computational overhead for the necessary optimization of…
We consider the inverse problem of the determining the potential in the dynamical Schr\"odinger equation on the interval by the measurement on the whole boundary. Provided that source is \emph{generic} using the Boundary Control method we…
Quantum optimal control has numerous important applications ranging from pulse shaping in magnetic-resonance imagining to laser control of chemical reactions and quantum computing. Our objective is to address two major challenges that have…
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…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…