Impact of time-retarded noise on dynamical decoupling schemes for qubits

TL;DR

This paper investigates how time-retarded noise affects the effectiveness of dynamical decoupling schemes, like CPMG, in prolonging qubit coherence, especially under different spectral densities relevant to superconducting qubits.

Contribution

It provides a rigorous numerical analysis of DD performance under time-nonlocal noise with varying spectral exponents, including comparisons with Ramsey and Hahn echo sequences.

Findings

Time-retarded noise significantly impacts DD effectiveness.

Spectral exponent s influences coherence times under DD.

DD schemes outperform free evolution and Hahn echo in certain regimes.

Abstract

One of the simplest and least resource-intensive methods to suppress decoherence for qubit operations, namely, dynamical decoupling (DD), is investigated for a broad range of realistic noise sources with time-retarded feedback. By way of example, the Carr-Purcell-Meiboom-Gill (CPMG) sequence is analyzed in a numerically rigorous manner accounting also for correlations between qubits and environments. Since experimentally noise sources are characterized through spectral densities, we adopt the spin-boson model as a suitable framework to describe the qubit dynamics under DD for a given spectral density $J(\omega) \propto \omega^s$. Motivated by the situation for superconducting qubits, the spectral exponent $s$ is varied from $s=1$ (Ohmic bath) to a substantially small value $0 < s \ll 1$ (deep sub-Ohmic bath), in order to investigate the impact of time-nonlocal back action on DD performances for enhanced coherence times. As reference to the DD schemes, dynamics of a single qubit subject to Ramsey sequences without any pules and Hahn echo (HE) sequences are also investigated.