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

arXiv: https://arxiv.org/abs/1907.02292 · HTML: https://mlsanity.com/paper/1907.02292/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [On exploring the potential of quantum auto-encoder for learning quantum systems](https://mlsanity.com/paper/2106.15432/) (2021)
- [Quantum Incremental Learning with Mixed State Prototypes](https://mlsanity.com/paper/2608.10464/) (2026)

## Abstract (arXiv)

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.