Quantum embeddings for machine learning

By Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh A. Izaac, Nathan Killoran. 2020

447 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4a7eea3ec3080ecb277bfe466afce4822a1071d7

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum Computing for Finance: State-of-the-Art and Future Prospects (2020, background): “A recent paper studies the embedding in the context of metric learning [108].”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, background): “Quantum Machine Learning Quantum machine learning (QML) [7], [25], [35], [37], [39], [40], [62] explores the training and evaluation of ML models on quantum devices.”
Effect of data encoding on the expressive power of variational quantum-machine-learning models (2020, background): “For example, it was remarked that data encoding determines the features that quantum models represent [23, 24], the decision boundaries they can learn [25], as well as the measurements that optimally distinguish between data classes [26].”
Quantum convolutional neural network for classical data classification (2021, background): “Lloyd et al. (2020).”
Challenges and opportunities in quantum machine learning (2022, background): “[22] Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh Izaac, and Nathan Killoran, “Quantum embeddings for machine learning,” arXiv preprint arXiv:2001.”
Quantum machine learning models are kernel methods (2021, methodology): “I will also consider the embedding ﬁxed and not trainable as proposed in [14, 18].”
The power of quantum neural networks (2020, background): “The choice of feature map is usually geared toward enhancing the performance of the quantum model and is typically neither optimised nor trained, though this idea was discussed in [37].”
Robust data encodings for quantum classifiers (2020, methodology): “[70] trains over hyperparameters using the re-uploading structure of Ref.”