Incoherent Control of Locally Controllable Quantum Systems

TL;DR

This paper introduces an incoherent control scheme for quantum systems that combines amplitude amplification, projective measurement, and unitary transformation to achieve control, demonstrated on a hydrogen atom example.

Contribution

It presents a novel three-step incoherent control scheme and algorithms for locally controllable quantum systems, linking control design with controllability analysis.

Findings

Control scheme effectively steers quantum states.

Projective measurements enhance control capabilities.

Applicable to systems with partial controllability information.

Abstract

An incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement on the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this eigenstate into the target state. Within this scheme, two control algorithms are presented for two classes of quantum systems. As an example, the incoherent control scheme is applied to the control of a hydrogen atom by an external field. The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems. Thus, this scheme establishes a subtle connection between control design and controllability analysis of quantum systems and provides an effective engineering approach for controlling quantum systems with partial controllability information.