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arXiv:1102.5115 · Physical Review A

Qubits as spectrometers of dephasing noise

Kevin C Young, K. Birgitta Whaley

Published Jul 13, 2012• 47 citations
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Abstract

We present a procedure for direct characterization of the dephasing noise acting on a single qubit by making repeated measurements of the qubit coherence under suitably chosen sequences of controls. We show that this allows a numerical reconstruction of the short-time noise correlation function and that it can be combined with a series of measurements under free evolution to allow a characterization of the noise correlation function over many orders of magnitude range in time scale. We also make an analysis of the robustness and reliability of the estimated correlation functions. Application to a simple model of two uncorrelated noise fluctuators using decoupling pulse sequences shows that the approach provides a useful route for the experimental characterization of dephasing noise and its statistical properties in a variety of condensed phase and atomic systems.

DOI
10.1103/physreva.86.012314

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We present a procedure for direct characterization of the dephasing noise acting on a single qubit by making repeated measurements of the qubit coherence under suitably chosen sequences of controls. We show that this allows a numerical reconstruction of the short-time noise correlation function and that it can be combined with a series of measurements under free evolution to allow a characterization of the noise correlation function over many orders of magnitude range in time scale. We also make an analysis of the robustness and reliability of the estimated correlation functions. Application to a simple model of two uncorrelated noise fluctuators using decoupling pulse sequences shows that the approach provides a useful route for the experimental characterization of dephasing noise and its statistical properties in a variety of condensed phase and atomic systems.
We propose a general method to characterize classical stochastic noise causing qubit dephasing through repetitive Ramsey interferometry measurements (RIMs) on the qubit. Compared to filter-function-based spectroscopy, our method with simpler pulse control is less constrained by probe coherence time and can directly detect arbitrary-order correlation functions of quasistatic noise processes. We show that each RIM with a short evolution time and suitably chosen control pulses directly samples the noise field and the nnn-point correlations of the RIM outcomes are proportional to the nnn-point correlation functions of the noise processes. We demonstrate the method numerically for two representative cases: an Ornstein-Uhlenbeck Gaussian process and a non-Gaussian ensemble of two-level fluctuators. While practical constraints such as readout contrast and sampling cost persist, our method offers a direct route to quasistatic classical noise spectroscopy across diverse platforms.
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 address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of a method for representing 1/ωα1/ω^α1/ωα noise developed by Kuopanportti et al. to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional control functions with bounded amplitude, that are capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during arbitrary one qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of 1/ω1/ω1/ω and constant offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to the noise offset, rendering them attractive for application to situations where homogeneous dephasing noise sources are accompanied by some extent of heterogeneous dephasing. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high fidelity single qubit gates are possible with current pulse generation technology.
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.
We address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of the method of Kuopanportti et al. [Phys. Rev. A 77, 032334 (2008)] for representing $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$ noise to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional, bounded amplitude control functions capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during one- and two-qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of $1/\ensuremath{\omega}$ and constant-offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to zero-frequency noise. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high-fidelity quantum gates may, in principle, be implemented for such qubits with the assistance of current pulse-generation technology.
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.