Optimisation-free Classification and Density Estimation with Quantum Circuits
This work addresses the challenge of efficient quantum machine learning for data analysis, though it appears incremental as it builds on existing quantum feature map concepts.
The paper introduces a quantum machine learning framework for classification and density estimation that maps data to quantum states and performs projections without optimizing circuit parameters, achieving results on a real quantum device.
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.