Minimum-Time Quantum Transport with Bounded Trap Velocity

TL;DR

This paper formulates and solves an optimal control problem for the minimum-time transport of a quantum particle in a harmonic trap with bounded velocity, providing a bang-bang control solution relevant for quantum computing and Bose-Einstein condensates.

Contribution

It introduces a complete solution to the minimum-time quantum transport problem with velocity constraints, revealing a bang-bang control strategy.

Findings

Optimal bang-bang control solution derived

Applicable to quantum information processing tasks

Potential extension to Bose-Einstein condensate transport

Abstract

We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system with bounded input. We completely solve the corresponding optimal control problem and obtain an interesting bang-bang solution. These results are expected to find applications in quantum information processing, where quantum transport between the storage and processing units of a quantum computer is an essential step. They can also be extended to the efficient transport of Bose-Einstein condensates, where the ability to control them is crucial for their potential use as interferometric sensors.