Universal control of quantum processes using sector-preserving channels

TL;DR

This paper formalizes the resource requirements and universal circuit architecture for coherent control of unknown and noisy quantum channels, extending control notions to higher dimensions and multiple channels.

Contribution

It introduces a resource-theoretic framework for controlling arbitrary quantum channels using sector-preserving channels and develops a universal circuit architecture for such control.

Findings

Identifies extended quantum channels as resources for control

Develops a universal circuit architecture for controlled channels

Introduces supermaps on routed channels for control representation

Abstract

No quantum circuit can turn a completely unknown unitary gate into its coherently controlled version. Yet, coherent control of unknown gates has been realised in experiments, making use of a different type of initial resources. Here, we formalise the task achieved by these experiments, extending it to the control of arbitrary noisy channels, and to more general types of control involving higher dimensional control systems. For the standard notion of coherent control, we identify the information-theoretic resource for controlling an arbitrary quantum channel on a $d$-dimensional system: specifically, the resource is an extended quantum channel acting as the original channel on a $d$-dimensional sector of a $(d+1)$-dimensional system. Using this resource, arbitrary controlled channels can be built with a universal circuit architecture. We then extend the standard notion of control to more general notions, including control of multiple channels with possibly different input and output systems. Finally, we develop a theoretical framework, called supermaps on routed channels, which provides a compact representation of coherent control as an operation performed on the extended channels, and highlights the way the operation acts on different sectors.