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Example for an implementation using wave propagation through a network of coupled modes (for example, optical resonators). Here detunings Δj of some of the optical modes are utilized as input x, whereas other detunings and coupling constants Jj between the modes are learnable parameters θ. The output is a suitable set of scattering matrix elements (equations (3) and (4)), which we obtain by comparing the response to the probe field (equation (2)).

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