Feature embedding


#1

hi,
I’m a bit confused about something.
let’s say that we have a vacuum state |0> and we would apply a Displacement gate or a Squeezing gate, is that considered a Hamiltonian encoding since we evolve the vacuum state based on the value of Dgate or Sgate?
Or is it amplitude encoding? @josh @Maria_Schuld

thanks


#2

I think this is a matter of taste and definition, but I’d rather describe it as something entirely different.

Amplitude encoding encodes a vector into the amplitude vector of a quantum state, Hamiltonian encoding encodes a matrix into the Hamiltonian of a quantum evolution. One could call the embedding induced by squeezing or displacement “Squeezing encoding/embedding” or “Displacement encoding/embedding”, since it encodes values into that respective property of a quantum state.


#3

so, let’s say that we want to establish a quantum kernel using a displaced squeezed state or just squeezing and then feed the “output” to a linear SVM. should the output be measured using the x-quadrature or photon counting or the inner product of the state itself
I’m just very curious about this since it was an open discussion during the quantum machine learning course on edx
@Maria_Schuld


#4

Well, again, this is up to you and what you want to try. But the canonical way would be to somehow let the quantum computer spit out the inner product of the two squeezed states. That would correspond to a feature map plus linear kernel.