# MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design

arXiv: https://arxiv.org/abs/2406.08591 · HTML: https://mlsanity.com/paper/2406.08591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm](https://mlsanity.com/paper/1910.02071/) (2019)
- [Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications](https://mlsanity.com/paper/1904.00176/) (2019)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [Learning Generative Models using Denoising Density Estimators](https://mlsanity.com/paper/2001.02728/) (2020)
- [Supervised Learning with Quantum Measurements](https://mlsanity.com/paper/2004.01227/) (2020)
- [Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection](https://mlsanity.com/paper/2211.03803/) (2022)
- [Quantum Adaptive Fourier Features for Neural Density Estimation](https://mlsanity.com/paper/2208.00564/) (2022)
- [AD-DMKDE: Anomaly Detection through Density Matrices and Fourier Features](https://mlsanity.com/paper/2210.14796/) (2022)
- [Fast Kernel Density Estimation with Density Matrices and Random Fourier Features](https://mlsanity.com/paper/2208.01206/) (2022)
- [InQMAD: Incremental Quantum Measurement Anomaly Detection](https://mlsanity.com/paper/2210.05061/) (2022)
- [Quantum Measurement Classification with Qudits](https://mlsanity.com/paper/2107.09781/) (2021)
- [Optimisation-free Classification and Density Estimation with Quantum Circuits](https://mlsanity.com/paper/2203.14452/) (2022)
- [LEAN-DMKDE: Quantum Latent Density Estimation for Anomaly Detection](https://mlsanity.com/paper/2211.08525/) (2022)

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

- [Quantum Machine Unlearning: Foundations, Mechanisms, and Taxonomy](https://mlsanity.com/paper/2511.00406/) (2025)

## Abstract (arXiv)

This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The model maps a training dataset to a quantum state represented by a density matrix through a quantum feature map. This training state encodes the probability distribution of the dataset in a quantum state, such that the density of a new sample can be estimated by projecting its corresponding quantum state onto the training state. We propose the application of a memetic algorithm to find the architecture and parameters of a variational quantum circuit that implements the quantum feature map, along with a variational learning strategy to prepare the training state. Demonstrations of the proposed strategy show an accurate approximation of the Gaussian kernel density estimation method through shallow quantum circuits illustrating the feasibility of the algorithm for near-term quantum hardware.