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arXiv:2304.05241 · Physical Review Letters

Nonergodic Measurements of Qubit Frequency Noise

Filip Wudarski, Yaxing Zhang, M. I. Dykman

Published Dec 6, 2023• 10 citations
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Abstract

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.

DOI
10.1103/physrevlett.131.230201

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Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.
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The paper describes the means to reveal and characterize slow periodic modulation of the qubit frequency. Such modulation can come from different sources and can impact qubit stability. We show that the modulation leads to very sharp peaks in the power spectrum of outcomes of periodically repeated Ramsey measurements. The positions and shapes of the peaks allow us to find both the frequency and the amplitude of the modulation. We also explore how additional slow fluctuations of the qubit frequency and fluctuations of the modulation frequency affect the spectrum. The analytical results are in excellent agreement with extensive simulations.
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A better understanding of the noise causing qubit decoherence is crucial for improving qubit performance. The noise spectrum affecting the qubit may be extracted by measuring dephasing under the application of pulse sequences but requires accurate qubit control and sufficiently long relaxation times, which are not always available. Here, we describe an alternative method to extract the spectrum from correlations of single-shot measurement outcomes of successive free induction decays. This method only requires qubit initialization and readout with a moderate fidelity and also allows independent tuning of both the overall sensitivity and the frequency region over which it is sensitive. Thus, it is possible to maintain a good detection contrast over a very wide frequency range. We discuss using our method for measuring both 1/f noise and the fluctuation spectrum of the nuclear bath of GaAs spin qubits.
Superconducting qubits have seen rapid increases in their coherence in the last few decades. However, instability in qubit parameters and their noise environment remains as a major challenge that limits the device performance. Qubit metrology to collectively measure and characterise different sources of noise and fluctuations is essential for accurately benchmarking devices but can be challenging, and typically different noise sources are characterised independently. In order to characterise the combined noise, we develop a tool that uses few-measurement data to detect and diagnose noise fluctuations, as well as a time series segmentation tool to further disambiguate different sources of fluctuations. We demonstrate the tool by computing time resolved properties of individual superconducting qubits. We find large changes of the dominating noise contributions, such as qubit frequency fluctuations, over both long time-scales of hours and days, and also over very short milli-seconds time-scales. We show that this information can be used alongside accurate noise models to learn physical properties of the coupled noise sources as well as benchmark device stability.
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.