Time-optimal bath-induced unitaries by Zermelo navigation: speed limit and non-Markovian quantum computation

TL;DR

This paper applies quantum Zermelo navigation to non-Markovian open systems, deriving a speed limit for environment-mediated unitaries and proposing a method for time-optimal quantum control in such systems.

Contribution

It introduces a framework for exact time-optimal realization of non-local unitaries in non-Markovian systems using Zermelo navigation, including a derived speed limit based on bath frequency.

Findings

Derived a speed limit for unitary implementation based on bath frequency

Presented a natural building block for constructing general unitaries via concatenation

Applied Zermelo navigation to non-Markovian quantum dynamics

Abstract

The solution of the quantum Zermelo navigation problem is applied to the non-Markovian open system dynamics of a set of quantum systems interacting with a common environment. We consider a case allowing an exact time-optimal realization of environment-mediated non-local system unitaries. For a linear coupling to a harmonic bosonic bath, we derive a speed limit for the implementation time in terms of the fundamental frequency of the bath modes. As a product of two exponentials of the local free wind and the pairwise system-coupling, the Zermelo unitary forms a natural building block for reaching a general unitary by concatenation.