Multifractality Analysis of Single Qubit Quantum Circuit Outcomes for a Superconducting Quantum Computer

TL;DR

The study investigates noise in near-term superconducting quantum devices by analyzing time series from repeated single-qubit circuits. Using wavelet leader-based multifractal analysis (WL-MFA) and bootstrap/surrogate testing, it reveals strong multifractality in measurement-outcome fluctuations, evidenced by a nonlinear zeta(q) and a broad D(h). This multifractal structure implies that quantum noise possesses scale-dependent patterns that could be exploited to design adaptive filtering and mitigation strategies. The findings contribute to a deeper understanding of quantum noise dynamics and offer a concrete pathway toward improved robustness of quantum computations on NISQ devices.

Abstract

We present a multifractal analysis of time series data obtained by repeatedly running a single-qubit quantum circuit on IBM superconducting quantum computers, in which the measurement outcomes are recorded as the number of zeros. By applying advanced signal processing techniques, including the wavelet leader method and multifractal detrended fluctuation analysis, we uncover strong multifractal behavior in the output data. This finding indicates that the temporal fluctuations inherent to quantum circuit outputs are not purely random but exhibit complex scaling properties across multiple time scales. The multifractal nature of the signal suggests the possibility of tailoring filtering strategies that specifically target these scaling features to effectively mitigate noise in quantum computations. Our results not only contribute to a deeper understanding of the dynamical properties of quantum systems under repeated measurement but also provide a promising avenue for improving noise reduction techniques in near-term quantum devices.

Figures (15)

• Figure 1: Single qubit quantum circuit used for the experiment saghafi2025predictive.
• Figure 2: Time series generated by repetitive executions of a quantum circuit in Figure \ref{['fig:cirqgraphs']}saghafi2025predictive.
• Figure 3: Autocorrelation function of the time series in Figure \ref{['fig:timeseries']}saghafi2025predictive
• Figure 4: Partial autocorrelation function of the time series in Figure \ref{['fig:timeseries']}saghafi2025predictive
• Figure 5: Fourier power spectrum of the positve frequencies on a log/log scale of the time series in Figure \ref{['fig:timeseries']}