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arXiv:1912.04982 · PRX Quantum

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

Uwe von Lüpke, Félix Beaudoin, Leigh Norris, Youngkyu Sung, Roni Winik, Jack Y. Qiu, Morten Kjærgaard, David K. Kim, Jonilyn Yoder, Simon Gustavsson, Lorenza Viola, William D. Oliver

Published Sep 3, 2020• 94 citations
arXivHTMLPDF

Abstract

Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology.However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far.We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation.By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features.Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables.While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures.By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments.

DOI
10.1103/prxquantum.1.010305

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Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology.However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far.We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation.By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features.Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables.While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures.By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments.
We introduce multipulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources. Our protocols are capable of reconstructing all the noise auto- and cross-correlation spectra entering the multiqubit dynamics, providing access, in particular, to the asymmetric spectra associated with nonclassical environments. Our result relies on (i) an exact analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control; (ii) the use of specific timing symmetries, which allow for a frequency comb to be engineered for all filter functions of interest, and for the spectra to be related to experimentally accessible observables. We show that quantum spectra have distinctive dynamical signatures, which we explore in two paradigmatic open-system models describing spin and charge qubits coupled to bosonic environments. Complete noise spectroscopy is demonstrated numerically in a realistic setting consisting of two-exciton qubits coupled to a phonon bath. The estimated spectra allow us to accurately predict the exciton dynamics as well as extract the temperature and spectral density of the quantum environment.
Spatiotemporally correlated errors are widespread in quantum devices and are particularly adversarial to error correcting schemes. To characterize these errors, we propose and validate a nonparametric quantum noise spectroscopy (QNS) protocol to estimate both spectra and static errors associated with spatiotemporally correlated dephasing noise and fluctuating quantum crosstalk on two qubits. Our scheme reconstructs the real and imaginary components of the two-qubit cross-spectrum by using fixed total time pulse sequences and single qubit and joint two-qubit measurements to separately resolve spatially correlated noise processes. We benchmark our protocol by reconstructing the spectra of spatiotemporally correlated noise processes engineered via the Schrödinger Wave Autoregressive Moving Average technique, emulating dephasing errors. Furthermore, we show that the protocol can outperform existing comb-based QNS protocols. Our results demonstrate the utility of our protocol in characterizing spatiotemporally correlated noise and quantum crosstalk in a multi-qubit device for potential use in noise-adapted control or error protection schemes.
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.
Spatially correlated noise poses a significant challenge to fault-tolerant quantum computation by breaking the assumption of independent errors. Existing methods such as cycle benchmarking and quantum process tomography can characterize noise correlations but require substantial resources. We propose straightforward and efficient techniques to detect and quantify these correlations by leveraging collective phenomena arising from environmental correlations in a qubit register. In these techniques, single-qubit state preparations, single-qubit gates, and single-qubit measurements, combined with classical postprocessing, suffice to uncover correlated relaxation and dephasing. Specifically, we use that correlated relaxation is connected to the superradiance effect, which we show to be accessible by single-qubit measurements. Analogously, the established parity oscillation protocol can be refined to quantify correlated dephasing without requiring the preparation of complex and entangled states.
Noisy quantum processors require precise and coherent quantum control to effectively execute quantum algorithms. Key to achieving precise control is the characterization of a quantum device to elucidate important details of environmentally-induced and systematic error sources. Quantum noise spectroscopy (QNS) is one such protocol used to characterize spatiotemporally correlated noise. QNS strives to provide estimates of noise statistical properties by using the quantum system as a dynamical probe. Despite its success, QNS can be challenging as it requires model selection prior to protocol implementation and suffers from scalability issues as system size grows. Here, we leverage machine learning to overcome model selection and assist in learning complex noise environments. In particular, we utilize physics-informed neural networks based on the “gray box” model to learn the dynamics of a two-qubit system subject to spatiotemporally correlated noise. Using training data sets based on dynamical decoupling, we show that the model is capable of learning the underlying power spectral densities for each qubit and the strength of parasitic qubit-qubit interactions. Furthermore, we show that the model can predict state-dependent behavior for multi-qubit observables. The results of this study further display the potential utility of machine learning to assist in the domain of quantum characterization and control.
We introduce Single-Shot Cross-Spectroscopy (SSCS), a method for extracting the auto- and cross-power spectral densities of dephasing noise in a qubit pair. The method uses straightforward input, namely, single-shot readouts from single-qubit Ramsey-type experiments, without requiring the reconstruction of qubit energy fluctuations from repeated measurements, and is resilient against errors in state preparation and measurement. We apply it to experimental data from a semiconductor spin-qubit device and obtain noise spectra over five orders of magnitude in frequency (5 mHz–500 Hz). Compared to other techniques, for spin qubits, SSCS enables access to noise correlations in the previously inaccessible intermediate-frequency range (1–500 Hz), and can be further extended with faster readout. The method is directly applicable to other qubit platforms, and the upper frequency it can probe is set by the repetition rate of a single-qubit preparation and measurement.