# Pattern recognition on the quantum Bloch sphere

arXiv: https://arxiv.org/abs/1603.00173 · HTML: https://mlsanity.com/paper/1603.00173/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2016.

## Built on by (most cited first, 6 of 6)

- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Kernel Density Matrices for Probabilistic Deep Learning](https://mlsanity.com/paper/2305.18204/) (2023)
- [Bayesian statistical learning using density operators](https://mlsanity.com/paper/2212.14715/) (2022)
- [FRQI Pairs method for image classification using Quantum Recurrent Neural Network](https://mlsanity.com/paper/2512.11499/) (2025)
- [QSMOTE-PGM/kPGM: QSMOTE Based PGM and kPGM for Imbalanced Dataset Classification](https://mlsanity.com/paper/2512.16960/) (2025)
- [From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers](https://mlsanity.com/paper/2607.15433/) (2026)

## Abstract (arXiv)

We introduce a framework suitable for describing pattern recognition task using the mathematical language of density matrices. In particular, we provide a one-to-one correspondence between patterns and pure density operators. This correspondence enables us to: i) represent the Nearest Mean Classifier (NMC) in terms of quantum objects, ii) introduce a Quantum Classifier (QC). By comparing the QC with the NMC on different 2D datasets, we show the first classifier can provide additional information that are particularly beneficial on a classical computer with respect to the second classifier.