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.
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.
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. We analyse empirical time series of repeated quantum circuit measurement outcomes from a superconducting NISQ processor, rather than eigenstates, wavefunctions or simulated quantum maps. We study shot‐aggregated measurement statistics (number of zeros per run over time) as a stochastic process influenced by hardware drift and measurement noise. By applying advanced signal processing techniques, including the wavelet leader method, we uncover strong multifractal behaviour 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.
Quantum computing holds the promise of transforming computational paradigms across science and engineering. But realizing potential on near term hardware demands on understanding of the noise processes that corrupt quantum circuit outputs. On superconducting processors, fragile qubits are continuously subjected to environmental disturbances including T1 relaxation, charge noise, and magnetic flux drift that cause measurement statistics to evolve in a nonstationary manner across repeated circuit executions, undermining the reliability of any result aggregated over a long experimental session. In this work, we treat the sequence of bitstring count outcomes from repeated executions of a fixed quantum circuit as a time series and conduct a systematic statistical investigation of its structure. The first contribution is constructing a predictive model of circuit output, demonstrating that future measurement outcomes can be forecast by exploiting temporal correlations in the execution record. We then extend the analysis to two circuits sharing the same physical qubit, examining cross-series dependencies and evaluating whether the drift behavior of one circuit can inform predictions about the other. The temporal structure of the signals is characterized in depth. The other contribution of this dissertation is to perform Wavelet-based multifractal analysis to reveal that quantum circuit outputs exhibit genuine multifractality. This is a hallmark of long range correlated, scale free processes rather than the simple Gaussian white noise assumed by standard error models. Complementary frequency-domain analysis identifies a residual 1/f noise component that persists after linear detrending, consistent with charge and flux noise mechanisms well documented in superconducting qubit literature. Motivated by these findings, The other contribution is to design and evaluate a suite of drift-mitigation filters including piecewise Huber regression, rolling median, smoothing spline, and Savitzky–Golay approaches under a rigorous chronological train/test protocol that mimics real operational deployment. The smoothing spline and median filter achieve near-zero corrected bias, while the rolling median emerges as the preferred solution for online, shot-by-shot correction due to its causal update structure and maximal robustness to impulsive hardware events. Taken together, our results characterize quantum circuit outputs as non-stationary, multifractal processes exhibiting long memory, seasonality, and inter-circuit causality, and establish a principled filtering framework for mitigating temporal bias drift in NISQ era quantum hardware.
Quantum computing promises a paradigm shift in computational power. However, a major challenge is mitigating the inherent noise and errors in quantum circuits. As quantum computers operate, their fragile qubits are highly susceptible to environmental disturbances, leading to errors that affect the outcomes of repeated circuit executions. Understanding and predicting these errors is crucial for improving the accuracy and reliability of quantum computing systems. In this work, we analyze and predict the output patterns of a single qubit quantum circuit by treating the results of repeated executions as a time series. Specifically, we collect measurement data from multiple runs of a quantum circuit and construct a time series from these observations. By training a predictive model, we aim to forecast future outcomes, providing insights into the error behavior of the quantum circuit. Additionally, we analyze time series data from two different circuits executed on the same qubit to investigate potential relationships and assess whether one dataset can be used to predict the other. Our findings reveal key characteristics of quantum circuit outputs, including stationarity, autocorrelation, seasonality, trends, linearity, and causality. The analysis highlights intriguing behaviors within the dataset. Furthermore, we evaluate multiple time series prediction methods and determine that XGBoost (Extreme Gradient Boosting) outperforms other approaches, demonstrating its effectiveness in accurately predicting quantum computing outputs in subsequent runs.
In quantum computing, characterizing the full noise profile of qubits can aid in increasing coherence times and fidelities by developing error-mitigating techniques specific to the noise present. This characterization also supports efforts in advancing device fabrication to remove sources of noise. Qubit properties can be subject to non-trivial correlations in space and time, for example, spin qubits in MOS quantum dots are exposed to noise originating from the complex glassy behavior of two-level fluctuator ensembles. Engineering progress in spin qubit experiments generates large amounts of data, necessitating analysis techniques from fields experienced in managing large data sets. Fields such as astrophysics, finance, and climate science use wavelet-based methods to enhance their data analysis. Here, we propose and demonstrate wavelet-based analysis techniques to decompose signals into frequency and time components, enhancing our understanding of noise sources in qubit systems by identifying features at specific times. We apply the analysis to a state-of-the-art two-qubit experiment in a pair of SiMOS quantum dots with feedback applied to relevant operation variables. The observed correlations serve to identify common microscopic causes of noise, such as two-level fluctuators and hyperfine coupled nuclei, as well as to elucidate pathways for multi-qubit operation with more scalable feedback systems.
We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture volatility asymmetry. Our results show that QCL-based volatility predictions preserve the negative return-volatility correlation, a hallmark of asymmetric volatility dynamics. Moreover, analysis of the Hurst exponent and multifractal characteristics indicates that the predicted series, like the original synthetic data, exhibits anti-persistent behavior and retains its multifractal structure.
Quantum devices in the noisy intermediate-scale quantum (NISQ) era are highly susceptible to different types of quantum noise, which directly impact the reliability of experimental results. This work provides a characterization of error behavior arising from quantum noises on IBM's superconducting quantum processor, offering practical insights for algorithm design, benchmarking, and error-mitigation strategies on a real superconducting quantum processor in the NISQ era. The study begins with the measurement of the basis state, without applying any gate, to quantify state-preparation and measurement (SPAM) errors. Additionally, the errors are further quantified due to the application of single-qubit Pauli-X, two-qubit CNOT gate and other multi-qubit Controlled-X gates. Each circuit was executed with 1024 shots, and the percentage error between the expected and observed outputs was computed. The results show that the single-qubit Pauli-X gate exhibits relatively low errors in comparison with the two-qubit CNOT gate, whereas other multi-qubit Controlled-X gates lead to significantly higher deviations. This work also analyzes the noise effect of a fourqubit Controlled-X gate being implemented using a three-qubit Controlled-X gate with an extra auxiliary qubit, and the result shows a significant reduction in the error rate.