Universality proof and analysis of generalized nested Uhrig dynamical decoupling

TL;DR

This paper proves the universality of nested Uhrig dynamical decoupling (NUDD) in quantum error suppression, analyzes its effectiveness against various errors, and predicts optimal sequence arrangements based on sequence parameters.

Contribution

It provides the first proof of NUDD's universality and offers a detailed analysis of how sequence parameters affect error suppression capabilities.

Findings

NUDD is universally effective for quantum error suppression.

Error suppression depends on the parities and magnitudes of nested UDD sequence orders.

Numerical simulations confirm the theoretical predictions.

Abstract

Nested Uhrig dynamical decoupling (NUDD) is a highly efficient quantum error suppression scheme that builds on optimized single axis UDD sequences. We prove the universality of NUDD and analyze its suppression of different error types in the setting of generalized control pulses. We present an explicit lower bound for the decoupling order of each error type, which we relate to the sequence orders of the nested UDD layers. We find that the error suppression capabilities of NUDD are strongly dependent on the parities and relative magnitudes of all nested UDD sequence orders. This allows us to predict the optimal arrangement of sequence orders. We test and confirm our analysis using numerical simulations.