Quantum computing has gained significant attention in recent years, with numerous algorithms and applications under active development. Limited by the current quantum technology, quantum noise and readout error have become critical issues. Various methods have been proposed to address readout error through error mitigation techniques, typically involving post-processing of measurement data. However, most of these methods increase the quantum hardware overhead, leading to higher computational costs. In this work, we present a machine-learning-based approach that minimizes hardware overhead while improving accuracy of the measurement probability distributions. We employed a convolutional neural network (CNN) autoencoder, commonly used for image denoising, as our baseline model. The datasets were derived from 4-qubit random circuits with depths ranging from 1 to 18, generated using Qiskit backends for target and noisy measurement data. The model was trained using mean squared error (MSE) as the loss function and Adam optimizer over 500 epochs, achieving an average noise reduction by 95% across the validation set, with no signs of overfitting. To validate the model's effectiveness across diverse quantum states, we conducted extensive tests on both typical quantum circuits and algorithms, including Grover's search algorithm, Quantum Fourier Transform, Haar random circuits and Trivial Paramagnet. The results demonstrated consistent and robust denoising in noisy measurement data, indicating that the autoencoder model is well-suited for efficient quantum error mitigation for current noisy quantum computers. This work contributes to the advancement of quantum error mitigation techniques using machine learning.
Quantum computing has gained significant attention in recent years, with numerous algorithms and applications under active development. Limited by the current quantum technology, quantum noise and readout error have become critical issues. Various methods have been proposed to address readout error through error mitigation techniques, typically involving post-processing of measurement data. However, most of these methods increase the quantum hardware overhead, leading to higher computational costs. In this work, we present a machine-learning-based approach that minimizes hardware overhead while improving accuracy of the measurement probability distributions. We employed a convolutional neural network (CNN) autoencoder, commonly used for image denoising, as our baseline model. The datasets were derived from 4-qubit random circuits with depths ranging from 1 to 18, generated using Qiskit backends for target and noisy measurement data. The model was trained using mean squared error (MSE) as the loss function and Adam optimizer over 500 epochs, achieving an average noise reduction by 95% across the validation set, with no signs of overfitting. To validate the model's effectiveness across diverse quantum states, we conducted extensive tests on both typical quantum circuits and algorithms, including Grover's search algorithm, Quantum Fourier Transform, Haar random circuits and Trivial Paramagnet. The results demonstrated consistent and robust denoising in noisy measurement data, indicating that the autoencoder model is well-suited for efficient quantum error mitigation for current noisy quantum computers. This work contributes to the advancement of quantum error mitigation techniques using machine learning.
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.
A quantum error mitigation technique based on machine learning is proposed, which learns how to adjust the probabilities estimated by measurement in the computational basis. Neural networks in two different designs are trained with random quantum circuits consisting of a set of one- and two-qubit unitary gates whose measurement statistics in the ideal (noiseless) and real (noisy) cases are known. Once the neural networks are trained, they infer the amount of probability adjustment to be made on the measurement obtained from executing an unseen quantum circuit to reduce the error. The proposed schemes are tested with two-, three-, five-, and seven-qubit quantum circuits of depth up to 20 by computer simulations with realistic error models and experiments using the IBM quantum cloud platform. In all test cases, the proposed mitigation technique reduces the error effectively. Our method can be used to improve the accuracy of noisy intermediate-scale quantum (NISQ) algorithms without relying on extensive error characterization or quantum error correction.
We present a systematic investigation of deep learning methods applied to quantum error mitigation of noisy output probability distributions from measured quantum circuits. We compare different architectures, from fully connected neural networks to transformers, and we test different design/training modalities, identifying sequence-to-sequence, attention-based models as the most effective on our datasets. These models consistently produce mitigated distributions that are closer to the ideal outputs when tested on both simulated and real device data obtained from IBM superconducting quantum processing units (QPU) up to five qubits. Across several different circuit depths, our approach outperforms other baseline error mitigation techniques. We perform a series of ablation studies to examine: how different input features (circuit, device properties, noisy output statistics) affect performance; cross-dataset generalization across circuit families; and transfer learning to a different IBM QPU. We observe that generalization performance across similar devices with the same architecture works effectively, without needing to fully retrain models.
Quantum computers have shown promise in improving algorithms in a variety of fields. The realization of these advancements is limited by the presence of noise and high error rates, which become prominent especially with increasing system size. Mitigation techniques using matrix inversions, unfolding, and deep learning, among others, have been leveraged to reduce this error. However, these methods are not reflective of the entire gate set of the quantum device and may need further tuning depending on the distance from the most recent calibration time. This paper proposes a method of improvement to numerical readout error techniques, where the readout error model is further refined using measured probability distributions from a collection of low-depth circuits. We use machine learning to improve the readout error model for the quantum system, testing the circuits on the simulated IBM Perth backend using Qiskit. We demonstrate a median 6.6% improvement in fidelity, 29.9% improvement for mean-squared error, and 10.3% improvement in Hellinger distance over the standard error mitigation approach for a seven-qubit system with a circuit depth of four. With further focus directed towards such improvement of these error mitigation techniques, we are one step closer to the fault-tolerant quantum computing era.
In this study, we present an innovative approach to quantum image classification, specifically designed to mitigate the impact of noise interference. Our proposed method integrates key technologies within a hybrid variational quantum neural network architecture, aiming to enhance image classification performance and bolster robustness in noisy environments. We utilize a convolutional autoencoder (CAE) for feature extraction from classical images, capturing essential characteristics. The image information undergoes transformation into a quantum state through amplitude coding, replacing the coding layer of a traditional quantum neural network (QNN). Within the quantum circuit, a variational quantum neural network optimizes model parameters using parameterized quantum gate operations and classical–quantum hybrid training methods. To enhance the system’s resilience to noise, we introduce a quantum autoencoder for error mitigation. Experiments conducted on FashionMNIST datasets demonstrate the efficacy of our classification model, achieving an accuracy of 92%, and it performs well in noisy environments. Comparative analysis with other quantum algorithms reveals superior performance under noise interference, substantiating the effectiveness of our method in addressing noise challenges in image classification tasks. The results highlight the potential advantages of our proposed quantum image classification model over existing alternatives, particularly in noisy environments.
The autoencoder is one of machine learning algorithms used for feature extraction by dimension reduction of input data, denoising of images, and prior learning of neural networks. At the same time, autoencoders using quantum computers are also being developed. However, current quantum computers have a limited number of qubits, which makes it difficult to calculate big data. In this paper, as a solution to this problem, we propose a computation method that applies a convolution filter, which is one of the methods used in machine learning, to quantum computation. As a result of applying this method to a quantum autoencoder, we succeeded in denoising image data of several hundred qubits or more using only a few qubits under the autoencoding accuracy of 98%, and the effectiveness of this method was obtained. Meanwhile, we have verified the feature extraction function of the proposed autoencoder by dimensionality reduction. By projecting the MNIST data to two-dimension, we found the proposed method showed superior classification accuracy to the vanilla principle component analysis (PCA). We also verified the proposed method using IBM Q Melbourne and the actual machine failed to provide accurate results implying high error rate prevailing in the current NISQ quantum computer.