Multiqubit spectroscopy of Gaussian quantum noise

Abstract

We introduce multi-pulse 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. We argue that this capability is crucial not only for metrological purposes, as it provides access to the asymmetric spectra associated with non-classical environments, but ultimately for achieving quantum fault-tolerance, as it enables the characterization of bath correlation functions. 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 in the control, 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 qubit 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 multiqubit 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. CONTENTS

Bayesian quantum noise spectroscopy

“…Different approaches to this problem, under different simplifying assumptions, have been proposed and even experimentally implemented [10,11,13,16,28]. More exotic protocols have been proposed to characterize more general noise processes, such as non-Gaussian noise [11] or noise affecting multiple qubits [12,29]. While we will not consider them here in detail, we note that the statistically motivated methods can in principle be also used there via an appropriate generalization.…”

“…From them, information about physical parameters of the bath can be extracted but only under concrete assumptions. For example, if one is given the prior that the bath consists of collection of harmonic oscillators in a thermal state and system and bath couple through linearly as in [12] then one can extract the temperature of the bath from S(ω).…”

“…At the other extreme-the small-data limit-a numerically stable Monte Carlo algorithm [18] approximates the full Bayesian solution. Our two approaches provide a robust solution to the software side of the noise spectroscopy problem, and can be used to improve state-of-the-art spectroscopy protocols [8][9][10][11][12]. These two regimes are schematically depicted in figure 1.…”

The dynamical-decoupling-based spatiotemporal noise spectroscopy

“…Using multiple entangled qubit to enhance the precision of spectroscopy of perfectly correlated noises was discussed in [41]. However, quantitative investigations of more general forms of crosscorrelations of multiple classical [37,42] and quantum noises [38,[42][43][44] (the term 'quantum noise' indicates a case when the interaction between the environment and qubits requires full quantum mechanical treatment as it cannot be approximated with an exposition to effective external stochastic process), have been subject to closer investigation only quite recently. Such investigations are currently of high importance for ongoing and nearfuture development of multi-qubit quantum registers for various applications.…”

A quantum spectrum analyzer enhanced by a nuclear spin memory

“…28,29 Multi-qubit probes may also assist the detection of cross-correlations in environmental noise 30 or the study of non-classical dynamics. 31 In recent experiments with spin qubits in diamond, auxiliary nuclear spins have been used to increase the effective coherence time of an electronic sensor spin by quantum error correction, 32 quantum feedback, 33,34 or by exploiting double-quantum coherence. 35 Moreover, ancillary nuclei have been used to enhance the readout efficiency.…”