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arXiv:2509.17723 · Advanced Quantum Technologies

Accelerated Characterization of Two‐Level Systems in Superconducting Qubits Via Machine Learning

Avinash Pathapati, Olli Mansikkamäki, Alexander Conkey Tyner, Alexander V. Balatsky

Published Mar 1, 2026• 0 citations
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Abstract

ABSTRACT We introduce a data‐driven approach for extracting two‐level system (TLS) parameters–frequency , coupling strength , dissipation time , and the pure dephasing time , labeled as a 4 component vector , directly from simulated spectroscopy data generated for a single TLS by a form of two‐tone spectroscopy. Specifically, we demonstrate that a custom convolutional neural network model(CNN) can simultaneously predict , , and from the spectroscopy data presented in the form of images. Our results show that the model achieves superior performance to perturbation theory methods in successfully extracting the TLS parameters. Although the model, initially trained on noise‐free data, exhibits a decline in accuracy when evaluated on noisy images, retraining it on a noisy dataset leads to a substantial performance improvement, achieving results comparable to those obtained under noise‐free conditions. Furthermore, the model exhibits higher predictive accuracy for parameters and in comparison to and .

DOI
10.1002/qute.202500868

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ABSTRACT We introduce a data‐driven approach for extracting two‐level system (TLS) parameters–frequency , coupling strength , dissipation time , and the pure dephasing time , labeled as a 4 component vector , directly from simulated spectroscopy data generated for a single TLS by a form of two‐tone spectroscopy. Specifically, we demonstrate that a custom convolutional neural network model(CNN) can simultaneously predict , , and from the spectroscopy data presented in the form of images. Our results show that the model achieves superior performance to perturbation theory methods in successfully extracting the TLS parameters. Although the model, initially trained on noise‐free data, exhibits a decline in accuracy when evaluated on noisy images, retraining it on a noisy dataset leads to a substantial performance improvement, achieving results comparable to those obtained under noise‐free conditions. Furthermore, the model exhibits higher predictive accuracy for parameters and in comparison to and .
Two-level systems (TLS) in superconducting quantum devices are a dominant source of decoherence, noise, and device variability, ultimately limiting qubit performance and scalability. Efficient and reliable extraction of TLS parameters from spectroscopy measurements is therefore essential for both device characterization and materials optimization. In this thesis, machine learning methods are developed to accelerate and enhance TLS characterization from superconducting qubit spectroscopy data. The approach combines physics-based simulation of driven qubit–TLS dynamics with supervised learning models trained on synthetic datasets to infer underlying physical parameters from two-dimensional spectroscopy maps. Particular emphasis is placed on understanding how different parameters are encoded in observable features, and on evaluating the extent to which the inverse problem is well-posed. The results demonstrate that machine-learning-assisted inference can significantly reduce the computational cost of parameter estimation compared to conventional fitting-based approaches, while maintaining high accuracy for spectrally encoded parameters such as TLS frequency and coupling strength. In contrast, decoherence parameters are shown to be intrinsically more challenging to extract from short-time spectroscopy data, highlighting fundamental limitations of the measurement protocol rather than the learning model. Overall, this work establishes a data-driven framework for scalable TLS characterization and provides insight into the interplay between physical observability and machine learning-based inference in quantum systems.
Introduction: The scalability of superconducting quantum processors is fundamentally limited by environmental noise and the exponential measurement overhead required for multi-qubit entanglement verification. Methods: In this work, we introduce a hybrid machine learning (ML) framework utilizing convolutional neural networks (CNNs) to simultaneously characterize decoherence channels and verify multipartite entanglement. The model is trained on synthetic noisy syndrome measurement data augmented with empirical SPAM models and applied to a 5-qubit superconducting device, where the neural network acts as a non-linear entanglement witness. Results: sweeps. Furthermore, it successfully verifies genuine multipartite entanglement with a fidelity prediction of 99.1%, while requiring only 12% of the measurement bases demanded by full quantum state tomography (QST). Discussion: Crucially, our methodology bypasses two distinct challenges: it drastically reduces the measurement complexity inherent in multi-qubit entanglement verification, and it inherently filters out state preparation and measurement (SPAM) errors without requiring noise-amplifying matrix inversions. These numerical results demonstrate that ML-assisted protocols provide a highly resource-efficient pathway for the characterization of noisy intermediate-scale quantum (NISQ) devices.
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and complex syndrome decoding, we propose a machine learning approach that directly reconstructs clean quantum states from noisy density matrices without additional qubits. We formulate quantum noise reduction as a supervised learning problem using a convolutional neural network (CNN) autoencoder architecture with a novel fidelity-aware composite loss function. Our method is trained and evaluated on a comprehensive synthetic dataset of 10,000 density matrices derived from random 5-qubit quantum circuits, encompassing five noise types (depolarizing, amplitude damping, phase damping, bit-flip, and mixed noise) across four intensity levels (0.05-0.20). The CNN successfully reconstructs quantum states across all noise conditions, achieving an average fidelity improvement from 0.298 to 0.774 (Δ = 0.476). Notably, the model demonstrates superior performance on complex mixed noise scenarios and higher noise intensities, with mixed noise showing the highest corrected fidelity (0.807) and improvement (0.567). The approach effectively preserves both diagonal elements (populations) and off-diagonal elements (quantum coherences), making it suitable for entanglement-dependent quantum algorithms. While phase damping presents fundamental information-theoretic limitations, our results suggest that CNN-based density matrix reconstruction offers a promising, resource-efficient alternative to traditional quantum error correction for NISQ-era devices. This data-driven approach could enable practical quantum advantage with fewer physical qubits than conventional error correction schemes require.
Abstract Convolutional neural network (CNN), as a prominent machine learning model, is crucial in image classification and feature extraction by completely utilizing the correlation information of data. Currently, the CNN is facing the challenges of slow computing speed, expanding data scale and poor interpretation for rapidly increasing Hilbert space. Fortunately, quantum convolutional neural network (QCNN) promises an elegant solution to improve the efficiency of data processing by combining the superiority of quantum computing and the feature extraction capability of the CNN. However, most of the existing QCNNs have the problem that they are feeble to extract global features effectively and coincidentally variational shadow quantum circuit (VSQC) can preferably figure out it. Accordingly, an enhanced QCNN assisted by the VSQC (VSQC‐QCNN) is developed. To be specific, the input data is primarily preprocessed by the VSQC module to establish global entanglement and extract effective features. Then the output shadow features are further processed by encoding, quantum circuit evolution and decoding through quantum convolutional layer and the dimensionality of the feature results is reduced through the pooling layer. When the data dimension is small enough, it is fed into a fully connected neural network to make classification predictions via activation functions. Experiments conducted on the MNIST dataset through the VQNet quantum framework demonstrate that the VSQC‐QCNN model is with performance surpassing the original QCNN in terms of loss function, classification accuracy and training speed. In addition, it is proved that the VSQC‐QCNN model has good astringency and stability under different circuit depths, widths and learning rates. Remarkably, the classification average accuracy of the model can reach up to 99% (even 100% for a few cases). Finally, experiments are also performed on Fashion‐MNIST and Iris datasets, indicating that the designed model has good universality.
Simulating non-Markovian quantum dissipative dynamics remains a major challenge in theoretical and computational chemistry. While traditional numerical methods such as hierarchical equations of motion are numerically exact, they suffer from prohibitive computational costs when modeling systems with complex environmental couplings or strong non-Markovian effects. To address this limitation, we propose a deep learning framework based on two-dimensional convolutional neural networks (2D-CNN) for efficiently predicting long-time quantum dissipative dynamics using only short-time trajectory data. Our approach incorporates a 1D-to-2D feature reconstruction strategy, which transforms 1D time-series data into 2D images, and a multi-timescale fusion network to resolve complex dynamical features. We validate the framework on two paradigmatic cases — dissipative relaxation in a two-level system and Rabi oscillations in a dissipative spin system — achieving prediction mean absolute errors of 10−310^{-3}10−3 and 10−2,10^{-2},10−2, respectively. The results highlight the effectiveness of our 2D-CNN approach in capturing long-time temporal correlations, providing a computationally efficient pathway for simulating quantum dynamics in realistic open systems.
Numerous studies have analyzed the use of hybrid quantum-classical convolutional neural networks as a promising alternative to classical deep learning. However, network components on quantum hardware impose fundamental limitations, while the scalability of quantum circuits leads to trainability issues. In this work, we investigate whether small, classically-emulated quantum circuit components can play a meaningful role within complex models, offering an alternative to purely classical convolutional architectures. To this end, we present a systematic study of the effectiveness of a Hybrid Quantum-inspired Convolutional Neural Network (HQiCNN) compared with a parameter-matched classical Convolutional Neural Network (CNN) that differs only in an intermediate dense neural layer. Both models are evaluated on two real-world medical datasets while systematically varying the different hyperparameters, ensuring a fair model comparison that is both dataset and hyperparameter independent. The results show that no architecture consistently dominates the other: the HQiCNN achieves its largest gains in intermediate-data regimes, whereas the CNN reaches the highest accuracies for the largest training sets in both datasets. Furthermore, removing entanglement produces comparable performance while enabling substantially better scalability of quantum simulations, and richer observable sets become beneficial only when sufficient training data are available. Finally, we propose two SHAP-based explainability tools for comparing the predictions between both models, ∣SHAP∣|SHAP|∣SHAP∣IoU and EMDposEMD_{pos}EMDpos​ metric, to demonstrate that both architectures consistently attend to anatomically plausible regions. Thus, we provide a comprehensive benchmark showing that, under certain conditions, hybrid quantum-inspired models are an alternative that can offer benefits in practical tasks such as medical image classification.