Unified Collision Model of Coherent and Measurement-based Quantum Feedback

TL;DR

This paper presents a unified framework using collision models to compare coherent and measurement-based quantum feedback, revealing their task-dependent advantages in quantum control.

Contribution

It introduces a general collision model framework that treats both feedback types equally and analyzes their effectiveness across various quantum control tasks.

Findings

Measurement-based feedback excels in cooling tasks.

Coherent feedback is more effective for quantum Hamiltonian control.

Both feedback types can simulate arbitrary Hamiltonian evolutions.

Abstract

We introduce a general framework, based on collision models and discrete CP-maps, to describe on an equal footing coherent and measurement-based feedback control of quantum mechanical systems. We apply our framework to prominent tasks in quantum control, ranging from cooling to Hamiltonian control. Unlike other proposed comparisons, where coherent feedback always proves superior, we find that either measurements or coherent manipulations of the controller can be advantageous depending on the task at hand. Measurement-based feedback is typically superior in cooling, whilst coherent feedback is better at assisting quantum operations. Furthermore, we show that both coherent and measurement-based feedback loops allow one to simulate arbitrary Hamiltonian evolutions, and discuss their respective effectiveness in this regard.