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arXiv:1803.07390 · Physical Review Applied

Measuring Environmental Quantum Noise Exhibiting a Nonmonotonic Spectral Shape

Y. Romach, A. Lazariev, I. Avrahami, F. Kleißler, S. Arroyo-Camejo, N. Bar-Gill

Published Jan 31, 2019• 17 citations
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Abstract

Quantum noise spectroscopy is an important tool for understanding the ubiquitous noise sources in quantum systems. Traditional spectroscopic methods are usually inefficient in measuring noise spectra that are broadband and decay nonmonotonically (exhibiting resonances, for example). Here a fresh approach uses a continuous driving method called gDYSCO. Performance of the continuous and traditional pulsed sequences is quantified analytically and numerically, and compared, revealing gDYSCO's advantages in reconstructing nontrivial spectral features. Experiments confirm the findings, pointing to improved understanding and handling of quantum noise sources through this superior technique.

DOI
10.1103/physrevapplied.11.014064

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Quantum noise spectroscopy is an important tool for understanding the ubiquitous noise sources in quantum systems. Traditional spectroscopic methods are usually inefficient in measuring noise spectra that are broadband and decay nonmonotonically (exhibiting resonances, for example). Here a fresh approach uses a continuous driving method called gDYSCO. Performance of the continuous and traditional pulsed sequences is quantified analytically and numerically, and compared, revealing gDYSCO's advantages in reconstructing nontrivial spectral features. Experiments confirm the findings, pointing to improved understanding and handling of quantum noise sources through this superior technique.
Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. While quantum noise spectroscopy has been employed in various quantum systems, such as superconducting qubits and trapped ions, traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and non-monotonous, thus posing a challenge to existing noise spectroscopy schemes.Here, we compared several methods for noise spectroscopy: spectral decomposition based on the CPMG sequence, the recently presented DYSCO sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO).The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth and sensitivity, revealing a supremacy of gDYSCO to reconstruct non-trivial features.Utilizing an ensemble of nitrogen-vacancy centres in diamond coupled to a high density 13C nuclear spin environment, we experimentally confirm our findings.The combination of the presented schemes offers potential to record high quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. Here we describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.
The fundamental assumption of dynamical-decoupling-based noise spectroscopy is that the coherence decay rate of qubit (or qubits) driven with a sequence of many pulses, is well approximated by the environmental noise spectrum spanned on frequency comb defined by the sequence. Here we investigate the precise conditions under which this commonly used spectroscopic approach is quantitatively correct. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian---both expected to be encountered when using the qubit for nanoscale nuclear resonance imaging. We have found that, in contrast to Lorentz spectrum, for which the corrections to the standard spectroscopic formulas can easily be made negligible, the spectra with finite range are more challenging to reconstruct accurately. For Gaussian line shape of environmental spectral density, direct application of the standard dynamical-decoupling-based spectroscopy leads to erroneous attribution of long-tail behavior to the reconstructed spectrum. Fortunately, artifacts such as this, can be completely avoided with the simple extension to standard reconstruction method.
Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we developed a method for dynamical decoupling noise spectroscopy. We generate effective filter functions that probe the environmental spectral density without requiring assumptions about its shape. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.
Precise environmental-noise characterisation in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Non-parametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra, (ii) control filter functions are no longer encumbered by time-ordering. In particular, we show that this approach enables the seamless generalisation of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that effectively remove time-ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.
Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a regularizer based on the total generalized variation (TGV) norm, in order to reconstruct a larger class of noise spectra, namely piecewise-linear noise spectra, which more realistically model many physical systems. We show through numerical simulations that the new method resolves finer spectral features, while maintaining an order-of-magnitude speedup over conventional approaches to noise spectroscopy. Second, we simplify the experimental implementation of the method, by introducing Rademacher measurements for reconstructing sparse noise spectra. These measurements use pseudorandom pulse sequences that can be generated in real time from a short random seed, reducing experimental complexity without compromising reconstruction accuracy. Together, these developments broaden the reach of random pulse sequences for accurate and efficient noise characterization in realistic quantum systems.