# Parallel Hybrid Networks: an interplay between quantum and classical neural networks

arXiv: https://arxiv.org/abs/2303.03227 · HTML: https://mlsanity.com/paper/2303.03227/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [When BERT Meets Quantum Temporal Convolution Learning for Text Classification in Heterogeneous Computing](https://mlsanity.com/paper/2203.03550/) (2022)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [Hybrid quantum neural network for drug response prediction](https://mlsanity.com/paper/2211.05777/) (2022)
- [Classical-to-Quantum Transfer Learning for Spoken Command Recognition Based on Quantum Neural Networks](https://mlsanity.com/paper/2110.08689/) (2021)
- [Benchmarking simulated and physical quantum processing units using quantum and hybrid algorithms](https://mlsanity.com/paper/2211.15631/) (2022)
- [Hybrid quantum ResNet for car classification and its hyperparameter optimization](https://mlsanity.com/paper/2205.04878/) (2022)
- [Quantum algorithms applied to satellite mission planning for Earth observation](https://mlsanity.com/paper/2302.07181/) (2023)
- [Practical application-specific advantage through hybrid quantum computing](https://mlsanity.com/paper/2205.04858/) (2022)

## Built on by (most cited first, 14 of 14)

- [Quantum machine learning for image classification](https://mlsanity.com/paper/2304.09224/) (2023)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)
- [Hybrid quantum image classification and federated learning for hepatic steatosis diagnosis](https://mlsanity.com/paper/2311.02402/) (2023)
- [Forecasting steam mass flow in power plants using the parallel hybrid network](https://mlsanity.com/paper/2307.09483/) (2023)
- [Hybrid quantum cycle generative adversarial network for small molecule generation](https://mlsanity.com/paper/2402.00014/) (2023)
- [A supervised hybrid quantum machine learning solution to the emergency escape routing problem](https://mlsanity.com/paper/2307.15682/) (2023)
- [Photovoltaic power forecasting using quantum machine learning](https://mlsanity.com/paper/2312.16379/) (2023)
- [Method for noise-induced regularization in quantum neural networks](https://mlsanity.com/paper/2410.19921/) (2024)
- [Quantum-Enhanced LLM Efficient Fine Tuning](https://mlsanity.com/paper/2503.12790/) (2025)
- [Parallel Multi-Circuit Quantum Feature Fusion in Hybrid Quantum-Classical Convolutional Neural Networks for Breast Tumor Classification](https://mlsanity.com/paper/2512.02066/) (2025)
- [Hybrid Quantum Neural Network Advantage for Radar-Based Drone Detection and Classification in Low Signal-to-Noise Ratio](https://mlsanity.com/paper/2403.02080/) (2024)
- [Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketches](https://mlsanity.com/paper/2407.06416/) (2024)
- [Soft-Quantum Algorithms](https://mlsanity.com/paper/2604.06523/) (2026)
- [QuantumBoostNet: Hybrid Classical-Quantum Cardiac View Identification](https://mlsanity.com/paper/2608.27302/) (2026)

## Abstract (arXiv)

Quantum neural networks represent a new machine learning paradigm that has recently attracted much attention due to its potential promise. Under certain conditions, these models approximate the distribution of their dataset with a truncated Fourier series. The trigonometric nature of this fit could result in angle-embedded quantum neural networks struggling to fit the non-harmonic features in a given dataset. Moreover, the interpretability of neural networks remains a challenge. In this work, we introduce a new, interpretable class of hybrid quantum neural networks that pass the inputs of the dataset in parallel to 1) a classical multi-layered perceptron and 2) a variational quantum circuit, and then the outputs of the two are linearly combined. We observe that the quantum neural network creates a smooth sinusoidal foundation base on the training set, and then the classical perceptrons fill the non-harmonic gaps in the landscape. We demonstrate this claim on two synthetic datasets sampled from periodic distributions with added protrusions as noise. The training results indicate that the parallel hybrid network architecture could improve the solution optimality on periodic datasets with additional noise.