Protecting qudit operations from noise by continuous dynamical decoupling

TL;DR

This paper introduces a generalized continuous dynamical decoupling method for protecting multi-qudit gates from noise, applicable to systems like hyperfine states of rubidium atoms, and extendable to ensembles of qudits.

Contribution

The paper develops a novel GCDD procedure for arbitrary qudits, demonstrating its implementation for a qutrit Hadamard gate and extension to multi-qudit ensembles.

Findings

GCDD can protect qudit operations from noise.

Model implementation using hyperfine states of rubidium.

Extension to ensembles of qudits.

Abstract

We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of $d$-level systems (qudits), allowing one to protect the action of an arbitrary multi-qudit gate from general noise. We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit. This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of $^{87}\mathrm{Rb}$ and laser beams whose intensities and phases are modulated according to our prescription. We show that this model allows one to generate continuously all the possible SU(3) group operations which are, in general, needed to apply the GCDD procedure. We finally show that our method can be extended to the case of an ensemble of qudits, identical or not.