Qubit noise spectroscopy using a continuous driving field

TL;DR

This paper investigates noise spectroscopy of qubits using continuous driving fields, comparing theoretical approaches and validating results with experiments, showing the method's robustness and agreement with pulsed techniques.

Contribution

It provides a rigorous analysis of noise spectroscopy with continuous fields, including higher-order corrections, and demonstrates experimental validation with solid-state NMR.

Findings

Heuristic filter function approach is qualitatively correct but quantitatively inaccurate.

0th-order average Hamiltonian matches generalized Bloch equation predictions.

CW and pulsed methods agree within experimental error in NMR experiments.

Abstract

The optimization of dynamical decoupling and quantum error correction for a particular qubit realization is based on a detailed knowledge of the noise properties. Spectroscopy of single-axis noise using dynamical decoupling pulse sequences has garnered much recent attention. Here we consider noise spectroscopy based on a spin-locking type pulse sequence, i.e. a continuous-wave (CW) on-resonance driving field. We show that a heuristic filter function approach produces a qualitatively correct (but quantitatively incorrect) result, whereas a 0th-order average Hamiltonian calculation is shown to agree with the result predicted by the generalized Bloch equations. We further calculate up to 2nd-order average Hamiltonian corrections and show the deviation from the generalized Bloch equation result. This shows that noise spectroscopy using continuous fields, in some cases simpler to implement and more robust to errors than pulsed schemes, can be rigorously analyzed and criteria for reliable measurements can be established. Finally, a solid-state nuclear magnetic resonance experiment is presented which demonstrates that the CW and pulsed methods agree within experimental error. The noise, due to magnetization fluctuations in a dipolar coupled proton spin bath, is found to obey a roughly 1/\omega\ power law decay in the range of frequencies \omega\ investigated.