Exploiting Non-Markovianity of the Environment for Quantum Control

TL;DR

This paper demonstrates how non-Markovian environments can be exploited to perform quantum control tasks that are impossible in isolated systems, using superconducting circuits and optimal control theory.

Contribution

It shows that non-Markovian effects enable implementing the full SU(N) group with limited control, expanding quantum control capabilities.

Findings

Non-Markovian environments enable new quantum control operations.

Optimal control achieves errors limited only by T1 relaxation.

Strongly coupled two-level systems induce non-Markovian effects.

Abstract

When the environment of an open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Here we show that this feature can be exploited to carry out quantum control tasks that could not be realized if the system was isolated. Inspired by recent experiments on superconducting phase circuits, we consider an anharmonic ladder with resonant amplitude control only. This restricts realizable operations to SO(N). The ladder is immersed in an environment of two-level systems. Strongly coupled two-level systems lead to non-Markovian effects, whereas the weakly coupled ones result in single-exponential decay. Presence of the environment allows for implementing diagonal unitaries that, together with SO(N), yield the full group SU(N). Using optimal control theory, we obtain errors that are solely $T_1$-limited.