This paper presents a strategy for efficient quantum circuit design for
density estimation. The strategy is based on a quantum-inspired algorithm
(DMKDE) 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.

本文提出了一种基于量子启发式算法（DMKDE）和基于群体智能算法的电路优化策略的高效量子电路设计方法，通过量子特征映射将训练数据集映射到由密度矩阵表示的量子态，以估计新样本的密度。所提出的策略通过浅层量子电路准确逼近高斯核密度估计方法，表明了该算法在近期量子硬件上的可行性。