Quantum Kernel Methods research spike

[andrewmusselman]

Overview

https://chat.openai.com/share/ba29ef75-4158-4e22-be40-78ae14c25f93

• What is output?
• Other gates needed?
• Other needed?
• Assess scope for implementing downstream quantum kernel calculations #458
• Add a Parameter object #468
• Parameterize R(X) #464
• Parameterize R(Y) #466
• Parameterize R(Z) #465
• Parameterize U #467
• Bind parameter values at execution #469
• Design data encoder solution #457
• Overlap measurements #476
• Swap test #477
• Post-processing #478

@tdnaugle:
The prototype squared dot product kernel calculation (my mahout fork) seems to work in both cirq and qiskit. The resulting state vector is expected to be zero since the two input vectors are orthogonal, and cirq yields zero, qiskit yields a very small number (due to simulation?).

I think next steps are to compare this example with the qiskit reference material and understand some answers to some elementary questions. For instance, what role do quantum circuits play in this simple step (kernel calculation) of a full Quantum Kernel ML algorithm?

@andrewmusselman:
I'll review this as well as the materials you found at https://github.com/PaddlePaddle/Quantum/blob/master/tutorials/machine_learning/QKernel_EN.ipynb