# QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization

arXiv: https://arxiv.org/abs/2110.11331 · HTML: https://mlsanity.com/paper/2110.11331/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [SpAtten: Efficient Sparse Attention Architecture with Cascade Token and Head Pruning](https://mlsanity.com/paper/2012.09852/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Defensive Quantization: When Efficiency Meets Robustness](https://mlsanity.com/paper/1904.08444/) (2019)
- [A Co-Design Framework of Neural Networks and Quantum Circuits Towards Quantum Advantage](https://mlsanity.com/paper/2006.14815/) (2020)
- [Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow](https://mlsanity.com/paper/2109.03430/) (2021)
- [Exploration of Quantum Neural Architecture by Mixing Quantum Neuron Designs](https://mlsanity.com/paper/2109.03806/) (2021)

## Built on by (most cited first, 27 of 27)

- [QOC: Quantum On-Chip Training with Parameter Shift and Gradient Pruning](https://mlsanity.com/paper/2202.13239/) (2022)
- [QuEst: Graph Transformer for Quantum Circuit Reliability Estimation](https://mlsanity.com/paper/2210.16724/) (2022)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers](https://mlsanity.com/paper/2311.16082/) (2023)
- [Diffusion-Inspired Quantum Noise Mitigation in Parameterized Quantum Circuits](https://mlsanity.com/paper/2406.00843/) (2024)
- [Sporadic Federated Learning Approach in Quantum Environment to Tackle Quantum Noise](https://mlsanity.com/paper/2507.12492/) (2025)
- [Hyperparameter Importance of Quantum Neural Networks Across Small Datasets](https://mlsanity.com/paper/2206.09992/) (2022)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [QuMoS: A Framework for Preserving Security of Quantum Machine Learning Model](https://mlsanity.com/paper/2304.11511/) (2023)
- [RobustAnalog: Fast Variation-Aware Analog Circuit Design Via Multi-task RL](https://mlsanity.com/paper/2207.06412/) (2022)
- [Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defenses](https://mlsanity.com/paper/2311.17458/) (2023)
- [PristiQ: A Co-Design Framework for Preserving Data Security of Quantum Learning in the Cloud](https://mlsanity.com/paper/2404.13475/) (2024)
- [Review of Ansatz Designing Techniques for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.04913/) (2022)
- [DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting](https://mlsanity.com/paper/2311.16214/) (2023)
- [QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks](https://mlsanity.com/paper/2211.07379/) (2022)
- [RobustState: Boosting Fidelity of Quantum State Preparation via Noise-Aware Variational Training](https://mlsanity.com/paper/2311.16035/) (2023)
- [JustQ: Automated Deployment of Fair and Accurate Quantum Neural Networks](https://mlsanity.com/paper/2403.11048/) (2024)
- [Security Concerns in Quantum Machine Learning as a Service](https://mlsanity.com/paper/2408.09562/) (2024)
- [EnQode: Fast Amplitude Embedding for Quantum Machine Learning Using Classical Data](https://mlsanity.com/paper/2503.14473/) (2025)
- [Finding Deviated Behaviors of the Compressed DNN Models for Image Classifications](https://mlsanity.com/paper/2112.02819/) (2021)
- [Graph Learning for Parameter Prediction of Quantum Approximate Optimization Algorithm](https://mlsanity.com/paper/2403.03310/) (2024)
- [ResQ: A Novel Framework to Implement Residual Neural Networks on Analog Rydberg Atom Quantum Computers](https://mlsanity.com/paper/2506.21537/) (2025)
- [Towards Quantum Machine Learning for Malicious Code Analysis](https://mlsanity.com/paper/2508.19381/) (2025)
- [ConQuER: Modular Architectures for Control and Bias Mitigation in IQP Quantum Generative Models](https://mlsanity.com/paper/2509.22551/) (2025)
- [Q-Bridge: Code Translation for Quantum Machine Learning via LLMs](https://mlsanity.com/paper/2603.27836/) (2026)
- [QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits](https://mlsanity.com/paper/2401.05571/) (2024)
- [Quantum Diffusion Models for Few-Shot Learning](https://mlsanity.com/paper/2411.04217/) (2024)

## Abstract (arXiv)

Parameterized Quantum Circuits (PQC) are promising towards quantum advantage on near-term quantum hardware. However, due to the large quantum noises (errors), the performance of PQC models has a severe degradation on real quantum devices. Take Quantum Neural Network (QNN) as an example, the accuracy gap between noise-free simulation and noisy results on IBMQ-Yorktown for MNIST-4 classification is over 60%. Existing noise mitigation methods are general ones without leveraging unique characteristics of PQC; on the other hand, existing PQC work does not consider noise effect. To this end, we present QuantumNAT, a PQC-specific framework to perform noise-aware optimizations in both training and inference stages to improve robustness. We experimentally observe that the effect of quantum noise to PQC measurement outcome is a linear map from noise-free outcome with a scaling and a shift factor. Motivated by that, we propose post-measurement normalization to mitigate the feature distribution differences between noise-free and noisy scenarios. Furthermore, to improve the robustness against noise, we propose noise injection to the training process by inserting quantum error gates to PQC according to realistic noise models of quantum hardware. Finally, post-measurement quantization is introduced to quantize the measurement outcomes to discrete values, achieving the denoising effect. Extensive experiments on 8 classification tasks using 6 quantum devices demonstrate that QuantumNAT improves accuracy by up to 43%, and achieves over 94% 2-class, 80% 4-class, and 34% 10-class classification accuracy measured on real quantum computers. The code for construction and noise-aware training of PQC is available in the TorchQuantum library.