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arXiv:1803.05538 · Physical Review A

Optimally band-limited spectroscopy of control noise using a qubit sensor

Leigh Norris, Dennis G. Lucarelli, Virginia Frey, Sandeep Mavadia, Michael J. Biercuk, Lorenza Viola

Published Sep 12, 2018• 45 citations
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Abstract

Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending nonparametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs single setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both single- and multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.

DOI
10.1103/physreva.98.032315

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Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending nonparametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs single setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both single- and multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.
Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. However, in common control routines out-of-band spectral leakage complicates interpretation of the sensor's signal. In this work, we leverage discrete prolate spheroidal sequences (a.k.a. Slepian sequences) to synthesize provably optimal narrowband controls ideally suited to spectral estimation of a qubit's noisy environment. Experiments with trapped ions demonstrate how spectral leakage may be reduced by orders of magnitude over conventional controls when a near resonant driving field is modulated by Slepians, and how the desired narrowband sensitivity may be tuned using concepts from RF engineering. We demonstrate that classical multitaper techniques for spectral analysis can be ported to the quantum domain and combined with Bayesian estimation tools to experimentally reconstruct complex noise spectra. We then deploy these techniques to identify previously immeasurable frequency-resolved amplitude noise in our qubit's microwave synthesis chain.
The fragility of quantum systems makes them ideally suited for sensing applications at the nanoscale. However, interpreting the output signal of a qubit-based sensor is generally complicated by background clutter due to out-of-band spectral leakage, as well as ambiguity in signal origin when the sensor is operated with noisy hardware. We present a sensing protocol based on optimally band-limited ``Slepian functions'' that can overcome these challenges, by providing narrowband sensing of ambient dephasing noise, coupling additively to the sensor along the zzz axis, while permitting isolation of the target noise spectrum from other contributions coupling along a different axis. This is achieved by introducing a finite-difference control modulation, which linearizes the sensor's response and affords tunable band-limited ``windowing'' in frequency. Building on these techniques, we experimentally demonstrate two spectral estimation capabilities using a trapped-ion qubit sensor. We first perform efficient experimental reconstruction of a ``mixed'' dephasing spectrum, composed of a broadband 1/f1/f1/f-type spectrum with discrete spurs. We then demonstrate the simultaneous reconstruction of overlapping dephasing and control noise spectra from a single set of measurements, in a setting where the two noise sources contribute equally to the sensor's response. Our approach provides a direct means to augment quantum-sensor performance in the presence of both complex broadband noise environments and imperfect control signals, by optimally complying with realistic time-bandwidth constraints.
The fragility of quantum systems makes them ideally suited for sensing applications at the nanoscale. However, interpreting the output signal of a qubit-based sensor is generally complicated by background clutter due to out-of-band spectral leakage, as well as ambiguity in signal origin when the sensor is operated with noisy hardware. We present a sensing protocol based on optimally band-limited Slepian functions that can overcome these challenges, by providing narrowband sensing of ambient dephasing noise, coupling additively to the sensor along the z{z}z-axis, while permitting isolation of the target noise spectrum from other contributions coupling along a different axis. This is achieved by introducing a finite-difference control modulation, which linearizes the sensor's response and affords tunable band-limited windowing in frequency. Building on these techniques, we experimentally demonstrate two spectral estimation capabilities using a trapped-ion qubit sensor. We first perform efficient experimental reconstruction of a mixed dephasing spectrum, composed of a broadband 1/f1/f1/f-type spectrum with discrete spurs. We then demonstrate the simultaneous reconstruction of overlapping dephasing and control noise spectra from a single set of measurements, in a setting where the two noise sources contribute equally to the sensor's response. Our approach provides a direct means to augment quantum-sensor performance in the presence of both complex broadband noise environments and imperfect control signals, by optimally complying with realistic time-bandwidth constraints.
We extend quantum noise spectroscopy (QNS) of amplitude control noise to settings where dephasing noise or detuning errors make significant contributions to qubit dynamics. Previous approaches to characterize amplitude noise are limited by their vulnerability to low-frequency dephasing noise and static detuning errors, which can overwhelm the target control noise signal and introduce bias into estimates of the amplitude noise spectrum. To overcome this problem, we leverage optimal control to identify a family of amplitude control waveforms that optimally suppress low-frequency dephasing noise and detuning errors, while maintaining the spectral concentration in the amplitude filter essential for spectral estimation. The waveforms found via numerical optimization have surprisingly simple analytic forms, consisting of oscillating sine waves obeying particular amplitude and frequency constraints. In numerically simulated QNS experiments, these waveforms demonstrate superior robustness, enabling accurate estimation of the amplitude noise spectrum in regimes where existing approaches are biased by low-frequency dephasing noise and detuning errors.
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.
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.