# Bernstein-Vazirani Networks: Quantum Machine Learning by Interference

arXiv: https://arxiv.org/abs/2608.19043 · HTML: https://mlsanity.com/paper/2608.19043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [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 Implicit Neural Representations](https://mlsanity.com/paper/2406.03873/) (2024)
- [Quantum perceptron over a field and neural network architecture selection in a quantum computer](https://mlsanity.com/paper/1602.00709/) (2016)
- [Quantum Visual Fields with Neural Amplitude Encoding](https://mlsanity.com/paper/2508.10900/) (2025)
- [Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from data](https://mlsanity.com/paper/2409.00172/) (2024)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)

## Abstract (arXiv)

We introduce Bernstein-Vazirani Networks (BVNs), a non-variational quantum machine learning framework that leverages quantum interference for supervised learning, demonstrated on vision and representation learning tasks. In their standard form, BVNs follow the principle of quantum Fourier sampling: labelled data are placed in superposition and interfered in the Fourier basis to extract globally informative features. We then define generalised BVNs that enable interference in problem-adapted bases, yielding more expressive models under the same measurement budget as in the standard setting. BVNs achieve universal function approximation through (over)complete interference bases, while training of BVNs is gradient-free. Experiments on synthetic and real-world classification tasks, as well as implicit image representation, show strong generalisation capabilities and competitive performance with classical and quantum baselines.