Exploiting Non-Markovianity for Quantum Control.

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 T1-limited.