Quantum Control at the Boundary
A. Balmaseda, J. M. Pérez-Pardo
TL;DR
The paper addresses the problem of controlling a quantum system by modifying boundary conditions on a finite interval, reframing boundary controls as a time-dependent Hamiltonian via a unitary gauge transformation. It analyzes a magnetic Laplacian model with quasi-periodic boundary conditions, proving well-posedness of the dynamics and establishing approximate controllability by leveraging Chambrion et al.'s results for linear quantum systems and a subsequent approximation argument to transfer controllability from an auxiliary to the original boundary-control system. The main contributions are the first rigorous demonstration of approximate controllability for boundary-controlled quantum systems and a clear demonstration of unitary equivalence to fixed-domain magnetic problems, enabling a tractable analysis. The findings imply that boundary-based quantum control is feasible with potential experimental implementations using flux-control in confined geometries, offering a novel route for quantum information processing and sensing.
Abstract
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove that this system is approximately controllable.