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International Symposium on Quality Electronic Design (ISQED)

QuEST: Quantum Circuit Output Estimation using Gaussian Distribution Analysis

Shamik Kundu, Navnil Choudhury, Kanad Basu

Published Apr 3, 2024• 1 citation
Publisher

Abstract

Quantum computing has holds considerable potential for accelerating computational tasks beyond the capabilities of classical computation. However, a major obstacle arises from the delicate nature of quantum hardware, where quantum gates and qubits, the fundamental components of a quantum circuit (QC), are vulnerable to external interference. Consequently, even a simple QC can produce significantly noisy output. This noise introduces uncertainty, making it difficult to ascertain whether the output represents meaningful computation or merely random noise. This uncertainty raises questions regarding the fidelity of a QC and the extent to which we can rely on its output. Existing classification-based approaches for output estimation have limitations, including the potential for incorrect results due to misclassification or the requirement for a large number of measurements, which can be expensive. To circumvent this, in this paper, we propose QuEST, which introduces an efficient technique for estimating the output of a QC by analyzing probability distributions of post-measurement data. Specifically, the QuEST framework employs Gaussian distribution functions to compare the measured distribution of a circuit with a pre-trained distribution obtained from a training circuit dataset. Moreover, we reformulate this problem by leveraging the properties of sequential time series, thereby deriving a straightforward and intuitive metric to measure the confidence of the QC output. By utilizing this metric, the QuEST framework monitors fidelity evolution over time as the QC interacts with its external environment, enabling the system to preemptively halt QC execution upon reaching a specified confidence threshold. When evaluated against state-of-the-art benchmark quantum circuits, our proposed QuEST framework accurately estimates the output of $100 \%$ of the benchmark circuits, while significantly achieving speedup up to $58.3 \times$ compared to a standard QC execution. These results highlight the efficiency of our framework and its potential for practical quantum computing applications.

DOI
10.1109/isqed60706.2024.10528722

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Context: The main obstacle of quantum computing on its way to scalability is the noisy nature of current hardware. Various types of errors lead to incorrect computational results,and measures such as quantum error mitigation are needed to counteract these errors. Many error mitigation techniques require a thorough understanding of the noise and its impact on computations. Therefore, accurate noise models are indispensable to facilitate meaningful quantum computing in the near future. They also enable realistic simulations of quantum devices. Since these devices are currently limited and quantum computing is expensive, researchers typically rely on simulations for testing their algorithms.Objective: In this thesis, we aim to construct a realistic noise model for quantum computing and optimise its model parameters. The model construction should build on the underlying physical processes, and the number of parameters should scale well with the system size. We also address the evaluation and comparison of different noise models by benchmarks using quantum circuits specific to real-world applications. Finally, we aim to develop useful graphical representations of noise models based on the existing quantum circuit model.Method: We present a benchmarking framework for quantum computing noise models and evaluate it based on benchmarking quality attributes from the literature. Moreover, we construct a quantum computing noise model and develop a training procedure for its parameters. We analyse the parameters of the trained noise model and the impact ofdifferent types of errors on computations. We benchmark the noise model with the above approach and compare it to a noise model provided by IBM’s software development kit Qiskit. Finally, we develop an extension of the quantum circuit model to represent noise channels.Result: The benchmarks performed in this thesis show that our noise model predicts noisy hardware behaviour of IBM’s ibmq_manila quantum device equally well as the Qiskit model, if not better, based on quantum circuits commonly used for variational quantum algorithms. Within the trained noise model, readout error has the most detrimental impact on computations. Our benchmarking approach satisfies relevant quality criteria by choosing suitable quantum circuits and objective functions to compare model predictionsto hardware data. Moreover, the quantum circuit model can be extended meaningfully by noise channels.Conclusion: Our benchmarking approach is suitable for evaluating and comparing quantum computing noise models. In future work, volumetric benchmarks should be performed for various noise models and application contexts. The parameter optimisation based on learning with training circuits yields accurate noise models and shows the importance of mitigating measurement error. Different optimisation algorithms and quantum circuits should be explored, and more types of noise should be incorporated into the noise model.

•Jan 12, 2026•0 citations
Quantum computing has holds considerable potential for accelerating computational tasks beyond the capabilities of classical computation. However, a major obstacle arises from the delicate nature of quantum hardware, where quantum gates and qubits, the fundamental components of a quantum circuit (QC), are vulnerable to external interference. Consequently, even a simple QC can produce significantly noisy output. This noise introduces uncertainty, making it difficult to ascertain whether the output represents meaningful computation or merely random noise. This uncertainty raises questions regarding the fidelity of a QC and the extent to which we can rely on its output. Existing classification-based approaches for output estimation have limitations, including the potential for incorrect results due to misclassification or the requirement for a large number of measurements, which can be expensive. To circumvent this, in this paper, we propose QuEST, which introduces an efficient technique for estimating the output of a QC by analyzing probability distributions of post-measurement data. Specifically, the QuEST framework employs Gaussian distribution functions to compare the measured distribution of a circuit with a pre-trained distribution obtained from a training circuit dataset. Moreover, we reformulate this problem by leveraging the properties of sequential time series, thereby deriving a straightforward and intuitive metric to measure the confidence of the QC output. By utilizing this metric, the QuEST framework monitors fidelity evolution over time as the QC interacts with its external environment, enabling the system to preemptively halt QC execution upon reaching a specified confidence threshold. When evaluated against state-of-the-art benchmark quantum circuits, our proposed QuEST framework accurately estimates the output of 100%100 \%100% of the benchmark circuits, while significantly achieving speedup up to 58.3×58.3 \times58.3× compared to a standard QC execution. These results highlight the efficiency of our framework and its potential for practical quantum computing applications.
Among different quantum algorithms, PQC for QML show promises on near-term devices. To facilitate the QML and PQC research, a recent python library called TorchQuantum has been released. It can construct, simulate, and train PQC for machine learning tasks with high speed and convenient debugging supports. Besides quantum for ML, we want to raise the community's attention on the reversed direction: ML for quantum. Specifically, the TorchQuantum library also supports using data-driven ML models to solve problems in quantum system research, such as predicting the impact of quantum noise on circuit fidelity and improving the quantum circuit compilation efficiency. This paper presents a case study of the ML for quantum part. Since estimating the noise impact on circuit reliability is an essential step toward understanding and mitigating noise, we propose to leverage classical ML to predict noise impact on circuit fidelity. Inspired by the natural graph representation of quantum circuits, we propose to leverage a graph transformer model to predict the noisy circuit fidelity. We firstly collect a large dataset with a variety of quantum circuits and obtain their fidelity on noisy simulators and real machines. Then we embed each circuit into a graph with gate and noise properties as node features, and adopt a graph transformer to predict the fidelity. Evaluated on 5 thousand random and algorithm circuits, the graph transformer predictor can provide accurate fidelity estimation with RMSE error 0.04 and outperform a simple neural network-based model by 0.02 on average. It can achieve 0.99 and 0.95 R2^22 scores for random and algorithm circuits, respectively. Compared with circuit simulators, the predictor has over 200X speedup for estimating the fidelity.
Abstract Fidelity is one of the most valuable and commonly used metrics for assessing the performance of quantum circuits on error-prone quantum processors. Several approaches have been proposed to estimate circuit fidelity without executing it on quantum hardware, but they often face limitations in scalability or accuracy. In this work, we present a comprehensive theoretical framework to predict the fidelity of quantum circuits under depolarizing noise. Building on theoretical results, we propose an efficient fidelity estimation algorithm based on device calibration data. The method is thoroughly validated through simulation and execution on real hardware, demonstrating improved accuracy compared to state-of-the-art alternatives, with enhancements in prediction R 2 ranging from 4.96% to 213.54%. The proposed approach provides a scalable and practical tool for benchmarking quantum hardware, comparing quantum software techniques such as compilation methods, obtaining computation bounds for quantum systems, and guiding hardware design decisions, making it a critical resource for developing and evaluating quantum computing technologies.
Evaluating the reliability of noisy quantum circuits is essential for implementing quantum algorithms on noisy quantum devices. However, current quantum hardware exhibits diverse noise mechanisms whose compounded effects make accurate and efficient reliability evaluation challenging. While state fidelity is the most faithful indicator of circuit reliability, it is experimentally and computationally prohibitive to obtain. Alternative metrics, although easier to compute, often fail to accurately reflect circuit reliability, lack universality across circuit types, or offer limited interpretability. To address these challenges, we propose a fine-grained, scalable, and interpretable framework for efficient and accurate reliability evaluation of noisy quantum circuits. Our approach performs a state-independent analysis to model how circuit reliability progressively degrades during execution. We introduce the Noise Proxy Circuit (NPC), which removes all logical operations while preserving the complete sequence of noise channels, thereby providing an abstraction of cumulative noise effects. Based on the NPC, we define Proxy Fidelity, a reliability metric that quantifies both qubit-level and circuit-level reliability. We further develop an analytical algorithm to estimate Proxy Fidelity under depolarizing, thermal relaxation, and readout error channels. The proposed framework achieves fidelity-level reliability estimation while remaining execution-free, scalable, and interpretable. Experimental results show that our method accurately estimates circuit fidelity, with an average absolute difference (AAD) ranging from 0.031 to 0.069 across diverse circuits and devices.
Quantum measurement is one of the critical steps in quantum computing that determines the probabilities associated with qubit states after conducting several circuit ex-ecutions and measurements. As a mesoscopic quantum system, real quantum computers are prone to noise. Therefore, a major challenge in quantum measurement is how to correctly inter-pret the noisy results of a quantum computer. While there are promising classification based solutions, they either produce incorrect results (misclassify) or require many measurements (expensive). In this paper, we present an efficient technique to estimate a qubit's state through analysis of probability distributions of post-measurement data. Specifically, we estimate the state of a qubit using cumulative distribution functions to compare the measured distribution of a sample with the distributions of basis states∣0⟩\vert 0\rangle∣0⟩and∣1⟩\vert 1\rangle∣1⟩. Our experimental results demonstrate a drastic reduction (78%) in single qubit readout error. It also provides significant reduction (12%) when used to boost existing multi-qubit discriminator models.
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.
Context: The main obstacle of quantum computing on its way to scalability is the noisy nature of current hardware. Various types of errors lead to incorrect computational results,and measures such as quantum error mitigation are needed to counteract these errors. Many error mitigation techniques require a thorough understanding of the noise and its impact on computations. Therefore, accurate noise models are indispensable to facilitate meaningful quantum computing in the near future. They also enable realistic simulations of quantum devices. Since these devices are currently limited and quantum computing is expensive, researchers typically rely on simulations for testing their algorithms.Objective: In this thesis, we aim to construct a realistic noise model for quantum computing and optimise its model parameters. The model construction should build on the underlying physical processes, and the number of parameters should scale well with the system size. We also address the evaluation and comparison of different noise models by benchmarks using quantum circuits specific to real-world applications. Finally, we aim to develop useful graphical representations of noise models based on the existing quantum circuit model.Method: We present a benchmarking framework for quantum computing noise models and evaluate it based on benchmarking quality attributes from the literature. Moreover, we construct a quantum computing noise model and develop a training procedure for its parameters. We analyse the parameters of the trained noise model and the impact ofdifferent types of errors on computations. We benchmark the noise model with the above approach and compare it to a noise model provided by IBM’s software development kit Qiskit. Finally, we develop an extension of the quantum circuit model to represent noise channels.Result: The benchmarks performed in this thesis show that our noise model predicts noisy hardware behaviour of IBM’s ibmq_manila quantum device equally well as the Qiskit model, if not better, based on quantum circuits commonly used for variational quantum algorithms. Within the trained noise model, readout error has the most detrimental impact on computations. Our benchmarking approach satisfies relevant quality criteria by choosing suitable quantum circuits and objective functions to compare model predictionsto hardware data. Moreover, the quantum circuit model can be extended meaningfully by noise channels.Conclusion: Our benchmarking approach is suitable for evaluating and comparing quantum computing noise models. In future work, volumetric benchmarks should be performed for various noise models and application contexts. The parameter optimisation based on learning with training circuits yields accurate noise models and shows the importance of mitigating measurement error. Different optimisation algorithms and quantum circuits should be explored, and more types of noise should be incorporated into the noise model.