Extending comb-based spectral estimation to multiaxis quantum noise

Abstract

We show how to achieve full spectral characterization of general multiaxis additive noise. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable even to models where a large qubit energy-splitting is present (as is typically the case for spin qubits in semiconductors, for example), as long as the noise is stationary and a second-order (Gaussian) approximation to the controlled reduced dynamics is viable. Our new result is crucial to extending the applicability of these protocols, now standard in dephasing-dominated platforms such as silicon-based qubits, to experimental platforms where both T1 and T2 processes are significant, such as superconducting qubits.

Relationship between subjecting the qubit to dynamical decoupling and to a sequence of projective measurements

“…In this work we show that such a close relationship between observables available in protocols based on multiple measurements, and the ones available after subjecting the qubit to dynamical decoupling, is much more general: it holds on the operational level without making any assumption on the initial state of the total system, the qubit-environment coupling, and the quantum or effectively classical nature of environmental dynamics affecting the qubit. We expect this result to contribute to the recently ongoing theoretical efforts aimed at understanding what information about quantum environment one can obtain from multiple measurements on the qubit [30,57,58], and at extending the DD-based noise spectroscopy paradigm to the case of general qubit-environment coupling [46].…”

Two-Qubit Spectroscopy of Spatiotemporally Correlated Quantum Noise in Superconducting Qubits

“…The Gaussian assumption may be satisfied exactly, for example for bosonic baths at equilibrium [48], or in an approximate sense when a large number of independent bath degrees of freedom are involved [49], or in any case the coupling is sufficiently weak for any higher-order cumulants to be negligible. It is worth noting that, from a rigorous spectral estimation standpoint, the assumptions of single-axis noise and Gaussianity cannot be expected to be valid a priori, and should always be verified experimentally through spectroscopic means [50][51][52]. While full characterization of a non-Gaussian noise source also requires higher-order spectral analogs of Eq.…”

“…While, as remarked, the present approach is developed under a rather generic set of assumptions on the target noise (i.e., that the latter is sufficiently weak, stationary, and predominantly dephasing in nature), generalized spin-locking protocols may also be anticipated under even less restrictive noise assumptions. In particular, in situations where T 1 and T 2 are comparable, the spectra of noise contributing to both dephasing and relaxation effects may be simultaneously reconstructed by leveraging a representation of the noise process in terms of its "spherical components" [52] and by fitting the solution of an appropriate ME to expectation values measured in a set of spin-locking experiments [67]. Likewise, by pushing the derivation of the TCL ME we present in Appendix A 1 to a higher order, it may be possible to extend the spin-locking technique to characterizing non-Gaussian noise (e.g., by reconstructing the noise bispectrum [50,51])-including nonclassical noise regimes that are attracting increasing attention [68].…”

“…Though a simultaneous characterization of all noise spectra S jk (ω) and S xx,j (ω) for all qubit axes would be much preferable in principle [52], the above approach, in which the effect of S xx,j (ω) is captured by a single parameter T (j ) 1 , has been successfully employed in a single-qubit context [32]. For sufficiently strong photon shot noise, longitudinal qubit relaxation effects are a significant, but weak correction that need only be taken into account at Rabi frequencies for which S jk (ω) is the weakest, i.e., at the tails of the Lorentzian spectra.…”

Characterization and control of open quantum systems beyond quantum noise spectroscopy

“…Fortunately, this limitation can in principle be overcome by quantum noise spectroscopy (QNS) protocols [1][2][3][4][5][6][7][8][9][10][11][12][13] . These protocols exploit the measurable response of the qubit to a known and variable control and the noise affecting it, in order to infer information about the noise.…”