# Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization

arXiv: https://arxiv.org/abs/2201.08629 · HTML: https://mlsanity.com/paper/2201.08629/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 21 Jan 2022.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [A Brief Introduction to Machine Learning for Engineers](https://mlsanity.com/paper/1709.02840/) (2017)
- [Quantum assisted Gaussian process regression](https://mlsanity.com/paper/1512.03929/) (2015)
- [A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification](https://mlsanity.com/paper/2201.01820/) (2022)
- [Stochastic Variational Optimization](https://mlsanity.com/paper/1809.04855/) (2018)

## Built on by (most cited first, 3 of 3)

- [Scalable Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2209.12372/) (2022)
- [3D Scalable Quantum Convolutional Neural Networks for Point Cloud Data Processing in Classification Applications](https://mlsanity.com/paper/2210.09728/) (2022)
- [Projection Valued Measure-based Quantum Machine Learning for Multi-Class Classification](https://mlsanity.com/paper/2210.16731/) (2022)

## Abstract (arXiv)

Quantum machine learning has emerged as a potential practical application of near-term quantum devices. In this work, we study a two-layer hybrid classical-quantum classifier in which a first layer of quantum stochastic neurons implementing generalized linear models (QGLMs) is followed by a second classical combining layer. The input to the first, hidden, layer is obtained via amplitude encoding in order to leverage the exponential size of the fan-in of the quantum neurons in the number of qubits per neuron. To facilitate implementation of the QGLMs, all weights and activations are binary. While the state of the art on training strategies for this class of models is limited to exhaustive search and single-neuron perceptron-like bit-flip strategies, this letter introduces a stochastic variational optimization approach that enables the joint training of quantum and classical layers via stochastic gradient descent. Experiments show the advantages of the approach for a variety of activation functions implemented by QGLM neurons.