# Negational Symmetry of Quantum Neural Networks for Binary Pattern Classification

arXiv: https://arxiv.org/abs/2105.09580 · HTML: https://mlsanity.com/paper/2105.09580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 20 May 2021.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Quantum Neuron: an elementary building block for machine learning on quantum computers](https://mlsanity.com/paper/1711.11240/) (2017)

## Built on by (most cited first, 1 of 1)

- [Machine Learning Applications of Quantum Computing: A Review](https://mlsanity.com/paper/2406.13262/) (2024)

## Abstract (arXiv)

Entanglement is a physical phenomenon, which has fueled recent successes of quantum algorithms. Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, for the time being, the effect of entanglement in QNNs and the behavior of QNNs in binary pattern classification are still underexplored. In this work, we provide some theoretical insight into the properties of QNNs by presenting and analyzing a new form of invariance embedded in QNNs for both quantum binary classification and quantum representation learning, which we term negational symmetry. Given a quantum binary signal and its negational counterpart where a bitwise NOT operation is applied to each quantum bit of the binary signal, a QNN outputs the same logits. That is to say, QNNs cannot differentiate a quantum binary signal and its negational counterpart in a binary classification task. We further empirically evaluate the negational symmetry of QNNs in binary pattern classification tasks using Google's quantum computing framework. The theoretical and experimental results suggest that negational symmetry is a fundamental property of QNNs, which is not shared by classical models. Our findings also imply that negational symmetry is a double-edged sword in practical quantum applications.