Quantum embeddings for machine learning

• URL: http://arxiv.org/abs/2001.03622v2
• Date: Mon, 10 Feb 2020 14:11:29 GMT
• Title: Quantum embeddings for machine learning
• Authors: Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh Izaac, Nathan Killoran
• Abstract summary: Quantum classifiers are trainable quantum circuits used as machine learning models. We propose to train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space. This approach provides a powerful analytic framework for quantum machine learning.
• Score: 5.16230883032882
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum classifiers are 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. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we 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 Helstrom 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.

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