Effect of pulse error accumulation on dynamical decoupling of the electron spins of phosphorus donors in silicon

TL;DR

This paper studies how pulse errors affect dynamical decoupling sequences in phosphorus donor electron spins in silicon, showing that concatenation can effectively suppress error accumulation and preserve quantum coherence.

Contribution

It provides a detailed analysis of pulse error accumulation and demonstrates that concatenated DD sequences can maintain high fidelity despite errors, with experimental validation.

Findings

Pulse errors can quickly destroy some spin states but preserve others.

Sequences based on x and y rotations outperform x and z sequences due to error accumulation.

Concatenation suppresses error accumulation, maintaining high fidelity across all spin components.

Abstract

Dynamical decoupling (DD) is an efficient tool for preserving quantum coherence in solid-state spin systems. However, the imperfections of real pulses can ruin the performance of long DD sequences. We investigate the accumulation and compensation of different pulse errors in DD using the electron spins of phosphorus donors in silicon as a test system. We study periodic DD sequences (PDD) based on spin rotations about two perpendicular axes, and their concatenated and symmetrized versions. We show that pulse errors may quickly destroy some spin states, but maintain other states with high fidelity over long times. Pulse sequences based on spin rotations about $x$ and $y$ axes outperform those based on $x$ and $z$ axes due to the accumulation of pulse errors. Concatenation provides an efficient way to suppress the impact of pulse errors, and can maintain high fidelity for all spin components: pulse errors do not accumulate (to first order) as the concatenation level increases, despite the exponential increase in the number of pulses. Our theoretical model gives a clear qualitative picture of the error accumulation, and produces results in quantitative agreement with the experiments.