A team of scientists at MIT and Xanadu has published a paper about quantum classifiers as trainable quantum circuits used as machine learning models.
The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space.
The second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. They have proposed to instead train the first part of the circuit—the embedding—with the objective of maximally separating data classes in Hilbert space, a strategy they call quantum metric learning.
As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrøm measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement.
This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.
