Dynamical Decoupling and Homogenization of continuous variable systems

TL;DR

This paper extends dynamical decoupling techniques to continuous variable quantum systems, specifically quadratic Hamiltonians, enabling suppression of decoherence and homogenization of harmonic oscillators, which was previously unestablished.

Contribution

It develops a dynamical decoupling method for continuous variable systems, introducing homogenization and providing bounds for effective decoherence suppression.

Findings

Homogenization maps interacting oscillators to non-interacting ones.

Decoherence can be suppressed with simple system-only operations.

Bounds are derived for the speed of dynamical decoupling schemes.

Abstract

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.