Experimental measurement of Hilbert-Schmidt distance between two-qubit states as means for speeding-up machine learning
This work addresses the need for efficient distance calculations in quantum machine learning, particularly for near-term quantum technologies, though it appears incremental as it builds on existing quantum interference techniques.
The authors tackled the problem of measuring distances between quantum states by experimentally measuring the Hilbert-Schmidt distance between two-qubit states using many-particle interference, resulting in a three-step method that is less complex than full density matrix reconstruction and applicable to quantum-enhanced machine learning for reducing computational complexity.
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.