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

Hanrui Wang¹, Jiaqi Gu², Yongshan Ding³, Zirui Li⁴, David Z. Pan³, Frederic T. Chong⁵, Song Han¹
¹MIT, ²University of Texas at Austin, ³Yale University, ⁴SJTU, ⁵University of Chicago
(* indicates equal contribution)


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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.

QuantumNAT framework overview:

QuantumNAT improves QNN accuracy on real quantum machines:



@inproceedings{wang2022quantumnat,  title={QuantumNAT: quantum noise-aware training with noise injection, quantization and normalization},  author={Wang, Hanrui and Gu, Jiaqi and Ding, Yongshan and Li, Zirui and Chong, Frederic T and Pan, David Z and Han, Song},  booktitle={Proceedings of the 59th ACM/IEEE Design Automation Conference},  pages={1--6},  year={2022}}


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We acknowledge NSF CAREER Award #1943349, MIT-IBM Watson AI Lab, Qualcomm Innovation Fellowship. This work is funded in part by EPiQC, an NSF Expedition in Computing, under grants CCF-1730082/1730449; in part by STAQ under grant NSF Phy-1818914; in part by DOE grants DE-SC0020289 and DE-SC0020331; and in part by NSF OMA-2016136 and the Q-NEXT DOE NQI Center. We acknowledge the use of IBM Quantum services for this work.

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