Microscopic treatment of instantaneous spectral diffusion and its effect on quantum gate fidelities in rare-earth-ion-doped crystals

TL;DR

This paper models the microscopic effects of instantaneous spectral diffusion (ISD) on quantum gate fidelity in rare-earth-ion-doped crystals, proposing methods to estimate and mitigate ISD errors for quantum computing.

Contribution

It introduces a stochastic microscopic model of ISD, a subsystem error estimation method, and strategies to suppress ISD errors in rare-earth-ion quantum systems.

Findings

ISD errors can be reduced using optical pumping to create transmission windows.

Despite suppression, a small probability (~0.3%) of large ISD errors remains.

Most ISD errors are smaller than other error sources, enabling NISQ algorithms.

Abstract

The effect of instantaneous spectral diffusion (ISD) on gate operations in rare-earth-ion-doped crystals is an important question to answer for the future of rare-earth quantum computing. Here we present a microscopic modeling that highlights the stochastic nature of the phenomenon, and use it to investigate ISD errors on single-qubit gate operations. Furthermore, we present a method to estimate the total error from many different error sources by only studying subsystems containing one error source at a time. This allows us to estimate the total ISD error from all non-qubit dopants in the vicinity of a qubit. We conclude that optical pumping techniques must be used to empty the frequency regions around the qubit transitions from absorption (transmission windows) in order to suppress the ISD errors. Despite using such windows, there remains a roughly $0.3\%$ risk that a qubit has an ISD error larger than the error from other sources. In those cases, the qubit can be discarded and its frequency channel can be reused by another qubit. However, in most cases the ISD errors are significantly smaller than other errors, thus opening up the possibility to perform noisy intermediate-scale quantum (NISQ) algorithms despite ISD being present.