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

TL;DR

This paper introduces MEMO-QCD, a novel quantum circuit design method using memetic algorithms for density estimation, enabling efficient and accurate quantum models suitable for near-term hardware.

Contribution

It proposes a memetic algorithm-based approach for optimizing quantum circuit architecture and parameters for density estimation tasks, combining quantum-inspired algorithms with variational learning.

Findings

Accurately approximates Gaussian kernel density estimation with shallow quantum circuits.

Demonstrates feasibility of the approach on near-term quantum hardware.

Provides a new method for quantum circuit design using memetic optimization.

Abstract

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.