# Experimental measurement of Hilbert-Schmidt distance between two-qubit states as means for speeding-up machine learning

## TL;DR

This paper experimentally measures the Hilbert-Schmidt distance between two-qubit states using many-particle interference, offering a simpler alternative to density matrix reconstruction for quantum machine learning applications.

## Contribution

It introduces a three-step method for measuring distances in Hilbert space that reduces complexity and can be applied to quantum-enhanced machine learning and quantum artificial intelligence.

## Key findings

- The method is less complex than density matrix reconstruction.
- It enables efficient distance measurement for quantum machine learning.
- Demonstrates the utility of mixed states in quantum information processing.

## Abstract

We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than reconstructing density matrices and that it can be applied in quantum-enhanced machine learning to reduce the complexity of calculating Euclidean distances between multidimensional points, which can be especially interesting for near term quantum technologies and quantum artificial intelligence research. Our results are also a novel example of applying mixed states in quantum information processing. Usually working with mixed states is undesired, but here it gives the possibility of encoding extra information as coherence between given two dimensions of the density matrix.