Extending comb-based spectral estimation to multiaxis quantum noise

Abstract

We show how to achieve full spectral characterization of general multiaxis additive noise on a single qubit, including arbitrary cross-axis noise correlations. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable in principle even to models where a large qubit energy splitting is present, as long as the noise is stationary and a second-order (Gaussian) approximation to the controlled reduced dynamics is viable. A key innovation in our approach is a spherical representation of the noise in terms of operators that couple directly to raising and lowering qubit operators, which is instrumental to show that only three suitably defined spectra effectively contribute in the large-splitting regime. Our result is crucial to extend the applicability of comb-based spectral estimation, which has been so far employed under the assumption of dephasing-dominated dynamics, to experimental platforms where both ${T}_{1}$ and ${T}_{2}$ processes may occur on comparable timescales or be otherwise significant, such as superconducting qubits.