# Continuous-variable quantum neural networks

arXiv: https://arxiv.org/abs/1806.06871 · HTML: https://mlsanity.com/paper/1806.06871/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2018.

## Built on by (most cited first, 30 of 74)

- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [projUNN: efficient method for training deep networks with unitary matrices](https://mlsanity.com/paper/2203.05483/) (2022)
- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [Slimmable Quantum Federated Learning](https://mlsanity.com/paper/2207.10221/) (2022)
- [Quantum Multi-Agent Meta Reinforcement Learning](https://mlsanity.com/paper/2208.11510/) (2022)
- [Exponentially Many Local Minima in Quantum Neural Networks](https://mlsanity.com/paper/2110.02479/) (2021)
- [Hybrid quantum convolutional neural networks model for COVID-19 prediction using chest X-Ray images](https://mlsanity.com/paper/2102.06535/) (2021)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [Quantum Neural Network Classifiers: A Tutorial](https://mlsanity.com/paper/2206.02806/) (2022)
- [Rapid training of quantum recurrent neural networks](https://mlsanity.com/paper/2207.00378/) (2022)
- [Fock State-enhanced Expressivity of Quantum Machine Learning Models](https://mlsanity.com/paper/2107.05224/) (2021)
- [A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification](https://mlsanity.com/paper/2201.01820/) (2022)
- [The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning](https://mlsanity.com/paper/2103.04913/) (2021)
- [QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2503.16678/) (2025)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Quantum Embedding Search for Quantum Machine Learning](https://mlsanity.com/paper/2105.11853/) (2021)
- [Completely Quantum Neural Networks](https://mlsanity.com/paper/2202.11727/) (2022)
- [Scalable Quantum Neural Networks for Classification](https://mlsanity.com/paper/2208.07719/) (2022)
- [QAmplifyNet: Pushing the Boundaries of Supply Chain Backorder Prediction Using Interpretable Hybrid Quantum-Classical Neural Network](https://mlsanity.com/paper/2307.12906/) (2023)
- [A Novel Spatial-Temporal Variational Quantum Circuit to Enable Deep Learning on NISQ Devices](https://mlsanity.com/paper/2307.09771/) (2023)
- [Arbitrary Polynomial Separations in Trainable Quantum Machine Learning](https://mlsanity.com/paper/2402.08606/) (2024)
- [Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus](https://mlsanity.com/paper/2510.06228/) (2025)
- [AutoQML: Automatic Generation and Training of Robust Quantum-Inspired Classifiers by Using Genetic Algorithms on Grayscale Images](https://mlsanity.com/paper/2208.13246/) (2022)
- [Quark: A Gradient-Free Quantum Learning Framework for Classification Tasks](https://mlsanity.com/paper/2210.01311/) (2022)
- [Projection Valued Measure-based Quantum Machine Learning for Multi-Class Classification](https://mlsanity.com/paper/2210.16731/) (2022)
- [Quantum Federated Learning with Entanglement Controlled Circuits and Superposition Coding](https://mlsanity.com/paper/2212.01732/) (2022)

## Abstract (arXiv)

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks.