QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization (2110.11331v4)

Abstract: 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.

• The paper introduces QuantumNAT, a comprehensive framework that mitigates noise in parameterized quantum circuits during both training and inference.
• It employs post-measurement normalization, strategic noise injection with realistic error gates, and quantization via a quadratic penalty to counteract hardware-induced noise effects.
• Empirical validation shows up to a 43% accuracy improvement across eight classification tasks on various quantum devices.

QuantumNAT: An Advanced Quantum Noise-Aware Training Framework

The paper details the development of QuantumNAT, a novel framework specifically designed to mitigate the performance degradation of Parameterized Quantum Circuits (PQC) on real quantum hardware, resulting from noise interference. This challenge is particularly pronounced in the Noisy Intermediate-Scale Quantum (NISQ) era, where error rates from quantum operations remain significantly high. QuantumNAT employs a comprehensive pipeline consisting of noise injection, quantization, and normalization strategies to enhance the robustness of Quantum Neural Networks (QNN), a form of PQC, during both training and inference phases.

Problem Context and Addressed Gaps

Quantum hardware, while progressing, still faces the setback of high noise rates, which severely impacts the utility of PQCs. For instance, experiments indicate an accuracy discrepancy exceeding 60% between noise-free simulations and actual outcomes on platforms like IBMQ-Yorktown for tasks such as MNIST-4 classification. While general noise mitigation methods have been explored, they fail to utilize the unique features of PQCs, resulting in limited applicability confined to the inference stage only. QuantumNAT differentiates itself by providing an all-encompassing solution that addresses both training and inference, inferring noise-induced discrepancies and optimally enhancing PQC robustness.

Methodological Innovations

QuantumNAT introduces a multi-faceted noise-aware optimization framework that notably elevates PQC performance through the following components:

1. Post-measurement Normalization: The framework innovatively maps the noise effect as a linear transformation of measurement outcomes, introducing a scaling and a shift factor that can be countered through normalization. This approach harmonizes outcome distributions between simulations and real-world noisy conditions by adjusting the variance and mean value of measurement results.
2. Noise Injection: To further bolster noise immunity, the training process is adapted through the random insertion of error gates, utilizing realistic noise models sourced from quantum hardware specifications. This mimicry of noise during training primes the PQC model for subsequent robustness in actual noisy environments, enhancing its resilience to quantum errors.
3. Post-measurement Quantization: By discretizing measurement outcomes into fixed-level buckets, QuantumNAT endeavors to minimize noise perturbations. The integration of a quadratic penalty loss reinforces the model’s ability to align measurement results near quantization centroids, counteracting the potential accumulation of noise deviations.

Empirical Validation

Empirically, QuantumNAT has demonstrated a substantial uptick in performance across eight classification tasks spanning six quantum devices. The improvements materialized as classification accuracies increased by margins of up to 43%, alongside maintaining commendable accuracy in varying classification complexities: over 94% for 2-class, 80% for 4-class, and 34% for 10-class on real quantum computers. The advantage of QuantumNAT is consistently evidenced across different model architectures and PQC design spaces.

Implications and Future Directions

Practically, QuantumNAT provides a resilient framework capable of functioning across different quantum hardware configurations, thus extending the achievable fidelity of quantum computations in practical settings. Theoretically, the methodological advancements made could catalyze further exploration into integration strategies for noise compensation within quantum circuits. Future developments might center on refining the adaptive aspects of noise modeling, potentially leveraging dynamic data to recalibrate error gate distributions.

The innovation introduced by QuantumNAT paves the way for more sophisticated noise mitigation techniques, enhancing the trajectory toward realizing quantum advantage in meaningful, computational tasks beyond classical feasibility. This endeavor is critical as the quantum research community strives to maximize the tangible benefits of PQCs in the context of noisy operational environments inherent to the current state of quantum technology.