Quantum Feature Spaces and Kernels

In this lecture, Kristan covers three topics. Firstly, the theory behind feature maps, feature spaces, and kernels is introduced. This is then expanded into the idea of a quantum feature space, accompanied by examples. Secondly, Kristan introduces the circuit for the quantum kernel estimation (QKE). Next, Kristan discusses near-term applications, including a specific algorithm that uses QKE, i.e. a classification algorithm. And thirdly, Kristan discusses the choice of circuit for the unitary feature map, $U(X)$. Constrains on entries to the kernel are considered, and comparisons between QKE and classical kernels are made.

Suggested links

• Download the lecturer's notes here

• Read about Supervised learning with quantum enhanced feature spaces

• Watch Kristan Temme on Supervised Learning with Quantum Enhanced Feature Spaces

• Read about Quantum machine learning in feature Hilbert spaces

• Read about A rigorous and robust quantum speed-up in supervised machine learning

FAQ

See https://strawberryfields.ai/photonics/demos/run_iqp.html for a more detailed explanation.

Other resources

• Read Vojtěch Havlíček, Antonio D. Córcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow & Jay M. Gambetta on Supervised learning with quantum-enhanced feature spaces

• Read Maria Schuld and Nathan Killoran on Quantum Machine Learning in Feature Hilbert Spaces