Using quantum theory to reduce the complexity of input-output processes

TL;DR

This paper demonstrates that quantum models can more efficiently simulate input-output processes than classical models by reducing unnecessary past information storage, highlighting the fundamental role of information theory in process complexity.

Contribution

The authors introduce quantum models that outperform classical ones in simulating input-output processes, reducing complexity by eliminating redundant past information.

Findings

Quantum models mitigate inefficiency in process simulation.

Classical models store unnecessary past information.

Quantum approach depends on the type of information theory used.

Abstract

All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic abstractions of their input-output behavior that allow us to simulate how such systems can behave in the future, conditioned on what has transpired in the past. Here, we show that classical models cannot avoid inefficiency -- storing past information that is unnecessary for correct future simulation. We construct quantum models that mitigate this waste, whenever it is physically possible to do so. This suggests that the complexity of general input-output processes depends fundamentally on what sort of information theory we use to describe them.