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.
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.
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.
This work focuses on the design and evaluation of Hybrid Quantum Neural Networks (HQNNs) that integrate the computational advantages of quantum circuits with the learning flexibility of classical deep neural networks to enhance machine learning performance in the Noisy Intermediate-Scale Quantum (NISQ) era.The study investigates two prominent HQNN architectures, namely Quantum Convolutional Neural Networks (QCNNs) and Quanvolutional Neural Networks (QuanNNs), with an emphasis on their robustness under realistic quantum noise conditions.It was evaluated using image classification tasks.Under various quantum noise channels, including Bit Flip, Phase Flip, Phase Damping, Amplitude Damping, and Depolarizing Noise, were introduced to reflect realistic hardware conditions.To reduce noise-induced performance loss, error mitigation techniques such as Zero-Noise Extrapolation, Probabilistic Error Cancellation, and Measurement Error Mitigation were applied.In addition, an AI-assisted adaptive framework is proposed to automatically recommend suitable mitigation strategies based on observed noise behavior and circuit characteristics.Experimental results indicate that QuanNN exhibits strong robustness under lowto-moderate noise levels and maintains stable performance even under high bit-flip noise, while QCNN demonstrates occasional performance gains under specific noisy configurations but degrades more rapidly as noise intensity increases.The proposed AI-guided mitigation mechanism further enhances model stability across varying noise regimes.This study provides practical insights into architecture selection, noise resilience, and intelligent error mitigation integration, offering a scalable framework for deploying HQNNs in real-world NISQ-era quantum machine learning applications.
Abstract Quantum noise is currently limiting efficient quantum information processing and computation, impacting on the fidelity and reliability of quantum states. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feed-forward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits undergoing noisy evolution, and we test its performance with both single-qubit (bit-flip, phase-flip, depolarizing, and amplitude damping) and two-qubit quantum channels (correlated amplitude damping). Furthermore, a critical aspect of our investigation involves also a comprehensive comparison between mean squared error and infidelity as loss functions. Our findings reveal that these two metrics yield comparable results in the context of state reconstruction. Moreover, we also consider the task of distinguishing between different quantum noisy channels, and show how a neural network-based classifier is able to solve such a classification problem with perfect accuracy.
Hybrid Quantum Neural Networks (HQNNs) offer promising potential of quantum computing while retaining the flexibility of classical deep learning. However, the limitations of Noisy Intermediate-Scale Quantum (NISQ) devices introduce significant challenges in achieving ideal performance due to noise interference, such as decoherence, gate errors, and readout errors. This paper presents an extensive comparative analysis of two HQNN algorithms, Quantum Convolutional Neural Network (QCNN) and Quanvolutional Neural Network (QuanNN), assessing their noise resilience across diverse image classification tasks. We systematically inject noise into variational quantum circuits using five quantum noise channels: Phase Flip, Bit Flip, Phase Damping, Amplitude Damping, and Depolarizing Noise. By varying noise probabilities from 0.1 to 1.0, we evaluate the correlation between noise robustness and model behavior across different noise levels.Our findings demonstrate that different noise types and levels significantly influence HQNN performance. The QuanNN shows robust performance across most noise channels for low noise levels (0.1 - 0.4), but succumbs to diverse effects of depolarizing and amplitude damping noise at probabilities between (0.5 - 1.0). However, the QuanNN exhibits robustness to bit flip noise at high probabilities (0.9 - 1.0). On the other hand, the QCNN tends to benefit from the noise injection by outperforming noise-free models for bit flip, phase flip, and phase damping at high noise probabilities. However, for other noise types, the QCNN shows gradual performance degradation as noise increases. These insights aim to guide future research in error mitigation strategies to enhance HQNN models in the NISQ era.
The pursuit of high-fidelity digital quantum simulation is fundamentally constrained by the inevitable presence of noise in current and near-term quantum processors. While quantum error correction ultimately promises fault-tolerance, its substantial qubit overhead renders it impractical for the noisy intermediate-scale quantum (NISQ) era. This research addresses the critical gap between hardware imperfections and simulation accuracy by designing systematic, resource-efficient machine learning (ML) error-mitigation protocols tailored specifically for digital quantum simulation. Unlike generic error-suppression methods, our approach exploits the unique structural properties of simulated quantum dynamics—including time-translation invariance, locality of interactions, and conserved quantities—to inform the training of lightweight neural networks and Gaussian process regressors. We develop a hybrid framework that combines randomized compiling with data-driven noise-inversion models, enabling real-time estimation and subtraction of both coherent and incoherent errors without exponential sampling overhead. Through extensive numerical benchmarks on spin-chain and Fermi-Hubbard models, we demonstrate that our ML protocols achieve up to an order-of-magnitude reduction in infidelity compared to standard probabilistic error cancellation and zero-noise extrapolation, while requiring fewer calibration circuits. Furthermore, we introduce an adaptive online learning scheme that continuously refines the mitigation model during the simulation runtime, automatically adjusting to time-dependent drift in hardware noise. Our results establish a practical pathway toward scalable, high-accuracy quantum simulations on existing devices, with implications for condensed matter physics, quantum chemistry, and the development of quantum advantage benchmarks.
Quantum computing offers exponential advantages for problems in cryptography, optimization, and quantum simulation, yet the practicality of current Noisy Intermediate-Scale Quantum (NISQ) devices is severely constrained by decoherence, gate imperfections, and measurement noise. Conventional quantum error correction (QEC) codes such as Steane and surface codes impose large qubit overheads and require high-fidelity logical operations, making them unsuitable for near-term hardware. To address this gap, this work introduces ML-QEM, an adaptive quantum error mitigation framework that employs machine learning to identify and correct dominant Pauli error patterns in real time using only 3–5 ancillary qubits. By integrating Qiskit Aer noise modeling with a lightweight TensorFlow-based classifier, ML-QEM learns device-specific noise characteristics and applies targeted recovery operations with minimal latency. Evaluations across depolarizing, amplitude damping, and thermal relaxation noise models demonstrate a 28.4% average fidelity improvement, 60–84% lower overhead than Steane and surface codes, and a classical processing delay of only 21.7 ms. ML-QEM thus provides an effective and resource-efficient pathway toward enhancing quantum computation fidelity in the NISQ era.