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

2025-12-20

AI Summary

This study investigates whether the zero-measurement count time series—generated by repeated executions of single-qubit circuits on IBM superconducting quantum processors—exhibit nontrivial multiscale scaling behavior beyond conventional stochastic noise assumptions. Method: We apply wavelet leaders multifractal analysis and multifractal detrended fluctuation analysis (MF-DFA) to rigorously characterize temporal fluctuations in the quantum output sequences. Contribution/Results: We provide the first empirical evidence that these quantum measurement sequences display statistically significant multifractality, revealing scale-dependent long-range correlations and heterogeneous fluctuations—features incompatible with simple white noise or Markovian models. This challenges standard quantum noise modeling paradigms and establishes a foundation for scale-adaptive filtering and novel fractal-feature-based quantum noise mitigation strategies. The findings offer both theoretical insight and experimental validation for enhancing the robustness and reliability of noisy intermediate-scale quantum (NISQ) devices.

Technology Category

• Machine Learning: Quantum Machine Learning
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• Analyzes multifractal behavior in quantum circuit outputs
• Investigates temporal fluctuations across multiple time scales
• Proposes noise mitigation strategies using scaling properties

Innovation

• Using wavelet leader method for multifractal analysis
• Applying multifractal detrended fluctuation analysis to quantum data
• Tailoring filtering strategies based on scaling features for noise mitigation