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IEEE Access

Predictive Time-Series Analysis of Single-Qubit Quantum Circuit Outcomes for a Superconducting Quantum Computer: Forecasting Error Patterns

Mohammadreza Saghafi, Lamine Mili

Published Jan 1, 2025• 5 citations
Publisher

Abstract

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.

DOI
10.1109/access.2025.3546259

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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 the context of current Noisy Intermediate-Scale Quantum (NISQ) computers, the application of quantum circuits is hampered by various sources of noise, resulting in errors between the actual output and the ideal output. To mitigate these errors, this study investigates a method for predicting the expected output of quantum circuits. In order to enhance the precision of the experiments, a fixed-scale quantum circuit dataset is randomly collected, and one-hot encoding is applied to represent the data. To eliminate redundant noise in the dataset, a Quantum auto-encoder (QAE) reconstruction encoding model is designed to separate and reconstruct the descriptions of quantum circuits in the dataset. The operation process of a quantum circuit is a sequence of quantum gate operations, and gate operations are gradually realized to change the state of qubits. We regard the process of quantum circuit implementation as a process of evolution with time, so it has the nature of timing. We build an additive fusion prediction model based on temporal neural network, the model can be trained to learn the relationship between sequences to predict the output of quantum circuit, and a loss function based on maximum likelihood estimation is employed to optimize the model parameters. Additionally, a dual approach is verified to optimize the computational indicators in the ensemble model. To validate the effectiveness of the proposed method, experiments are conducted on quantum circuits of varying scales, and the results are compared with the quantum system framework provided by IBM Quantum Experience. The experimental results show that the time series neural network integration can better highlight timing information and noise information in quantum circuits, the proposed method outperforms the IBM Quantum Experience framework in terms of circuit depth and network depth for quantum circuits of different scales, exhibiting robustness and stability.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.
Multiple layers of the quantum system full-stack require data on temporal variations in error rates of physical elements. The absence of this information, especially when users access cloud-based quantum systems with waiting queues between compilation and execution, can lead to unreliable computations due to outdated calibration data. One example is the compilation process that impacts the success rate of quantum circuits. This paper proposes using five machine learning and time-series models to predict error rate variability for two-qubit gates based on calibration data. We compare model accuracy and complexity in terms of execution time. The predicted information is applied to a noise-aware compiler to evaluate the impact on success rate. Experimental results on a real superconducting quantum processor demonstrate accurate predictions of temporal error rate variability, achieving performance comparable to that of real calibration data, reducing the impact of queue waiting times that can reach up to two days.
Time series forecasting is a critical problem with applications in various fields, such as finance, energy, and environmental science. While classical machine learning methods have shown significant progress in this domain, the advent of quantum machine learning introduces a new perspective to address the complexities of time series prediction. In this research, we propose a novel Quantum Neural Network (QNN) approach for time series forecasting, leveraging the unique capabilities of quantum computing to capture intricate temporal dependencies and exploit quantum parallelism. By encoding time series data into quantum states and designing quantum circuits for processing, the QNN aims to achieve improved predictive accuracy compared to classical neural networks. Through extensive experiments on diverse time series datasets, we demonstrate the potential of our QNN framework and discuss the future prospects of quantum-powered time series prediction in real-world applications.
Time series forecasting has always been a thought-provoking topic in the field of machine learning. Machine learning scientists define a time series as a set of observations recorded over consistent time steps. And, time series forecasting is a way of analyzing the data and finding how variables change over time and hence, predicting the future value. Time is of great essence in this forecasting as it shows how the data coordinates over the dataset and the final result. It also requires a large dataset to ascertain the regularity and reliability. Quantum computers may prove to be a better option for perceiving the trends in the time series by exploiting quantum mechanical phenomena like superposition and entanglement. Here, we consider one-step time series forecasting using variational quantum circuits, and record observations for different datasets.
The increasing focus on long-term time series prediction across various fields has been significantly strengthened by advancements in quantum computation. In this paper we introduce a data-driven method designed for time series prediction with quantum dynamical embedding (QDE). This approach enables a trainable embedding of the data space into an extended state space, allowing for the recursive retrieval of time series information. Based on its independence of time series length, this method achieves depth-efficient quantum circuits that are crucial for near-term quantum computers. Numerical simulations demonstrate the model's capability to predict not only wave signals but also more complex signals such as NARMA. Prediction accuracy improves with model scaling, and notably, the model achieves better accuracy on wave signal tasks with fewer parameters compared to QRC. Additionally, the model shows promising potential for denoising classical noise in wave signals, and when combined with error mitigation techniques for typical quantum noise, it enables reliable long-term prediction of wave signals. We implement this model, restricted to two qubits, on the Origin ``Wukong'' superconducting quantum processor as a simple proof of concept on NISQ devices. Furthermore, we provide theoretical analysis of the QDE's dynamical properties for the two-qubit case and discuss its potential universality. Overall, this study represents our first step towards leveraging near-term quantum devices for time series forecasting, offering insights into integrating data-driven learning with quantum dynamical embeddings.