# Optimisation-free Classification and Density Estimation with Quantum Circuits

arXiv: https://arxiv.org/abs/2203.14452 · HTML: https://mlsanity.com/paper/2203.14452/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 65 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 19 of 19)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [A divide-and-conquer algorithm for quantum state preparation](https://mlsanity.com/paper/2008.01511/) (2020)
- [VSQL: Variational Shadow Quantum Learning for Classification](https://mlsanity.com/paper/2012.08288/) (2020)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Optimal training of variational quantum algorithms without barren plateaus](https://mlsanity.com/paper/2104.14543/) (2021)
- [Revisiting dequantization and quantum advantage in learning tasks](https://mlsanity.com/paper/2112.00811/) (2021)
- [Supervised Learning with Quantum Measurements](https://mlsanity.com/paper/2004.01227/) (2020)
- [Efficient decomposition of unitary matrices in quantum circuit compilers](https://mlsanity.com/paper/2101.02993/) (2021)
- [Fast Black-Box Quantum State Preparation](https://mlsanity.com/paper/2009.10709/) (2020)

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

- [MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design](https://mlsanity.com/paper/2406.08591/) (2024)

## Abstract (arXiv)

We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework.