Temporally correlated flux-induced phase noise can influence superconducting-quantum-circuit execution in ways that are not fully captured by uncorrelated, memoryless, or gate-averaged noise models. In this work, we develop an execution-oriented, circuit-level workflow for modeling and evaluating such effects. The workflow combines source-specific circuit-level noise components with a phenomenological segmented correlation-time construction for flux-induced phase noise, thereby enabling explicit control of a tunable correlation-time parameter τc within a composite circuit-level noise model. Using a single-qubit Carr-Purcell-Meiboom-Gill (CPMG) sequence and standard randomized benchmarking as the representative single-qubit circuit settings, we evaluate how circuit outputs respond to temporally correlated flux-induced phase noise under otherwise matched simulation conditions. The results show that temporally correlated flux-induced phase noise produces circuit-level behavior that differs qualitatively from uncorrelated or memoryless descriptions, and that its impact is governed jointly by the correlation-time parameter τc, the temporal structure of the circuit, and the way in which the circuit samples the noise. The proposed workflow provides a circuit-level framework for analyzing temporally correlated noise in superconducting quantum computing.
Temporally correlated flux-induced phase noise can influence superconducting-quantum-circuit execution in ways that are not fully captured by uncorrelated, memoryless, or gate-averaged noise models. In this work, we develop an execution-oriented, circuit-level workflow for modeling and evaluating such effects. The workflow combines source-specific circuit-level noise components with a phenomenological segmented correlation-time construction for flux-induced phase noise, thereby enabling explicit control of a tunable correlation-time parameter τc within a composite circuit-level noise model. Using a single-qubit Carr-Purcell-Meiboom-Gill (CPMG) sequence and standard randomized benchmarking as the representative single-qubit circuit settings, we evaluate how circuit outputs respond to temporally correlated flux-induced phase noise under otherwise matched simulation conditions. The results show that temporally correlated flux-induced phase noise produces circuit-level behavior that differs qualitatively from uncorrelated or memoryless descriptions, and that its impact is governed jointly by the correlation-time parameter τc, the temporal structure of the circuit, and the way in which the circuit samples the noise. The proposed workflow provides a circuit-level framework for analyzing temporally correlated noise in superconducting quantum computing.
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.
Combining tensor network techniques with quantum autoregressive moving average models, we quantify the effects of time-correlated noise on quantum algorithms and predict their performance at scale. As a paradigmatic test case, we examine the quantum Fourier transformation. Building on our first technical result, which shows how stochastic tensor network calculations capture frequency correlations, our second result is the revelation that infidelity exponents (scaling from diffuse, to superdiffuse) are determined by the spectral features of the noise. This numerical result rigorously quantifies the common belief that the temporal correlation scale is a key predictive feature of noise's deleterious impact on multi-qubit circuits. To highlight prospects for predicting algorithmic performance, our third result quantifies how infidelity scaling exponents -- which are fits determined by training data at moderate scales (40-80 qubits) -- can be used to predict more computationally expensive simulation at larger scales (100-128 qubits). Aside from highlighting the scalability of our methods, this workflow feeds into our last result, which is the proposal of predictive benchmarking protocols connecting simulations to experiments. Our work paves the way for large-scale algorithmic simulations and performance prediction under hardware-relevant noise conditions informed by realistic device characteristics.
Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunable temporal correlations, we identify a clear signature of error correlations between sequential gates in randomly composed quantum circuits, and extract quantitative measures linked to the underlying noise correlation length. By replacing all gates in these circuits with "virtual" dynamically corrected gates (DCGs), we demonstrate that even in the presence of strongly correlated noise the signatures of error correlations between sequential gates appear similar to standard gates exposed to uncorrelated noise. A theoretical model applied to our experiments reveals that common DCGs suppress the correlated error component by over 270× with 95% confidence. Using block-correlated noise, we explore the scaling of the effective error correlation length at the virtual level, and show that DCGs exhibit error correlations indistinguishable from those arising from uncorrelated noise.
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.
Classical simulation of noisy quantum circuits is essential for validating algorithms, benchmarking hardware, and assessing error-mitigation strategies, but remains limited by the exponential cost of density-matrix methods and the high variance of standard trajectory sampling. We introduce a variance-aware tensor network framework that combines the tensor jump method with local TDVP gate evolution on matrix product states and sparse Pauli-Lindblad hardware noise models. Gates are applied as short variational evolutions on the MPS manifold, while noise is sampled per circuit window from Pauli-Lindblad jump sets with state-independent hazards and dissipative contractions that reduce to irrelevant global factors after renormalization. The method supports correlated multi-qubit Lindblad noise consistent with hardware connectivity, including long-range operators on non-adjacent qubits, enabling direct simulation of crosstalk and other connectivity-induced errors beyond local noise models. We develop two unbiased variance-aware unravelings. An analog unitary-mixture unraveling matches the Lindblad generator exactly under symmetric Gaussian or two-point angle laws, while a projector-jump unraveling yields state-independent hazards and closed-form variance laws. Both retain the standard 1/sqrt(N) Monte Carlo convergence but with reduced prefactors. Empirically, projector sampling strongly reduces trajectory variance and bond-dimension growth across many circuit architectures, whereas analog sampling is most effective at weak noise. We demonstrate accurate, scalable noisy-circuit simulation on a 25-qubit noisy XY quench and IBM's 127-qubit kicked-Ising benchmark with long-range depolarizing noise, achieving reduced Monte Carlo variance and favorable MPS bond-dimension growth compared with standard Kraus-insertion baselines.
Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.