On the complexity of controlling quantum many-body dynamics

TL;DR

This paper shows that reversing the dynamics of quantum many-body systems is possible with partial control and is robust to noise, providing bounds on control complexity related to system integrability.

Contribution

It introduces a method for reversing quantum many-body dynamics with partial control and analyzes the control complexity in relation to system integrability.

Findings

Reversal of quantum dynamics is feasible with partial Hamiltonian control.

Reversed dynamics exhibit high robustness to external noise.

Control complexity is bounded by the manifold dimension of the system.

Abstract

We demonstrate that arbitrary time evolutions of many-body quantum systems can be reversed even in cases when only part of the Hamiltonian can be controlled. The reversed dynamics obtained via optimal control --contrary to standard time-reversal procedures-- is extremely robust to external sources of noise. We provide a lower bound on the control complexity of a many-body quantum dynamics in terms of the dimension of the manifold supporting it, elucidating the role played by integrability in this context.