Qubit Noise Spectroscopy for Non-Gaussian Dephasing Environments

Abstract

We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.

Multiqubit spectroscopy of Gaussian quantum noise

“…First, as remarked in [14], although a general spectrum S(ω) is asymmetric about ω = 0, only the even contribution S + 1,1 (ω) ≡ S(ω) + S(−ω) enters the dynamics (and can thus be reconstructed) in generic single-qubit dephasing scenarios. Second, noise may exhibit non-trivial spatial correlations, which may only become manifest in the coherence dynamics of multiple qubit probes at different locations.…”

“…It should also be highlighted that the comb approximation for both G ± a,a ;b,b (ω, M T ) holds only if the spectrum appearing in the convolution does not diverge at any point, implying that only sufficiently smooth power spectra can be reconstructed [14].…”

“…An important factor to consider when building the base sequences is the presence of experimentally motivated constraints. Following our work in [14], we consider two: the minimum switching time τ 0 and the time resolution δ. The former captures the fact that there is a finite pulse bandwidth, resulting in an unavoidable minimal waiting time between the application of two pulses.…”

“…Characterization of discrete non-Gaussian phase noise has, likewise, been implemented in trapped ions [25], whereas general QNS protocols for reconstructing high-order spectra of non-Gaussian classical and quantum dephasing environments have been proposed in [14]. Central to QNS protocols is the idea that, by suitably tailoring the external control, and hence the FFs describing the ensuing modulation in the frequency domain, one may engineer a frequency comb which makes it possible to "deconvolve" the effect of the noise and sample a desired spectrum at a set of control-dependent harmonic frequencies.…”

Quantum Sensing of Noisy and Complex Systems under Dynamical Control

“…Since dynamical decoupling (DD) techniques have also been recently employed in noise spectroscopy [82][83][84][85][86][87][88][89], in the wake of our pioneering work [10,11,[13][14][15][16][17][18][19] it is appropriate to compare the two approaches.…”