Quantum Geometry of Data

TL;DR

This paper introduces Quantum Cognition Machine Learning (QCML), which encodes data into quantum geometric structures like Hilbert space states, revealing rich global geometric properties that enhance data analysis and cognitive modeling.

Contribution

The paper presents a novel quantum geometric framework for data representation in machine learning, integrating quantum concepts with data analysis to capture global dataset properties.

Findings

QCML encodes data as quantum states with rich geometric structure

Demonstrates effectiveness on synthetic and real-world datasets

Potential to improve understanding of cognitive phenomena through quantum models

Abstract

We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum geometry description endows the dataset with rich geometric and topological structure - including intrinsic dimension, quantum metric, and Berry curvature - derived directly from the data. QCML captures global properties of data, while avoiding the curse of dimensionality inherent in local methods. We illustrate this on a number of synthetic and real-world examples. Quantum geometric representation of QCML could advance our understanding of cognitive phenomena within the framework of quantum cognition.