# Canonical quantization of neurons

arXiv: https://arxiv.org/abs/2607.05000 · HTML: https://mlsanity.com/paper/2607.05000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Quantum Neuron: an elementary building block for machine learning on quantum computers](https://mlsanity.com/paper/1711.11240/) (2017)
- [Quantum Perceptron Models](https://mlsanity.com/paper/1602.04799/) (2016)
- [Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models](https://mlsanity.com/paper/1609.02542/) (2016)
- [Quantum Boltzmann machine learning of ground-state energies](https://mlsanity.com/paper/2410.12935/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Natural gradient and parameter estimation for quantum Boltzmann machines](https://mlsanity.com/paper/2410.24058/) (2024)
- [An Artificial Spiking Quantum Neuron](https://mlsanity.com/paper/1907.06269/) (2019)
- [Fermi-Dirac thermal measurements: A framework for quantum hypothesis testing and semidefinite optimization](https://mlsanity.com/paper/2603.04061/) (2026)
- [Coherent Feed Forward Quantum Neural Network](https://mlsanity.com/paper/2402.00653/) (2024)
- [Natural Quantization of Neural Networks](https://mlsanity.com/paper/2503.15482/) (2025)
- [Fermi-Dirac machines as quantizations of neurons](https://mlsanity.com/paper/2605.24386/) (2026)

## Abstract (arXiv)

Canonical quantization provides a systematic procedure for constructing quantum models from classical Hamiltonians. Here, we apply this principle to a fundamental computational primitive of machine learning: the neuron. Specifically, by viewing a neuron as a composition of an energy function and an activation function, we quantize this model by replacing the energy function with a quantum Hamiltonian and applying the activation function to it through matrix functional calculus. This results in an activation observable that can be measured on an input quantum state. We investigate the use of these quantized neurons for function approximation, where the objective is to learn an unknown observable from labeled quantum data. For this purpose, we develop hybrid quantum-classical algorithms for training and evaluation, including procedures for measuring the activation observable and estimating gradients of the squared loss error. Our algorithms for gradient estimation rely on basic primitives like classical random sampling, the Hadamard test, and Hamiltonian simulation, and those for measuring an activation observable rely on quantum algorithms known as the power of one qumode and Schroedingerization. Numerical experiments demonstrate that our quantized neurons exhibit enhanced expressive capabilities relative to corresponding classical neurons on representative learning tasks. Our work establishes canonical quantization as a principled framework for constructing quantum machine learning primitives and provides a foundation for developing neural architectures tailored to quantum data.