Table 1 Summary of the differences between classical ELMs and QELMs.

From: Potential and limitations of quantum extreme learning machines

 

ELM

QELM

Training data

\({\{({{{{{{{{\boldsymbol{x}}}}}}}}}_{k},{{{{{{{{\boldsymbol{y}}}}}}}}}_{k})\}}_{k}\)

\({\{({\rho }_{k},{{{{{{{{\boldsymbol{y}}}}}}}}}_{k})\}}_{k}\)

Model to train

x ↦ Wf(x)

ρ ↦ WpΛ,μ(ρ)

Parameters to train

W

W

Cost function

∥yk − Wf(xk)∥2

∥yk − WpΛ,μ(ρk)∥2

  1. These two schemes differ in the type of input states ρk fed to the reservoir, and in how the reservoir map itself is implemented: in the classical case, is some nonlinear function often implemented via fixed-weights neural network architectures, whereas in the quantum case it is a quantum channel followed by some measurement.
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