Efficacy of noisy dynamical decoupling

TL;DR

This paper analyzes the effectiveness of dynamical decoupling in quantum systems with noisy pulses, revealing conditions under which it mitigates errors and limits to its scalability.

Contribution

It provides a detailed analysis of noisy dynamical decoupling, establishing breakeven conditions and identifying the limits of concatenated DD in error mitigation.

Findings

DD only mitigates errors when noise from pulses is less than background noise

There are specific breakeven conditions for DD effectiveness

Concatenated DD has a performance limit due to accumulated noise

Abstract

Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here, we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD, and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses do not outweigh the increased ability in averaging away the original background noise. We present breakeven conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.