Fig. 1: The overview of training formalism for the parameterized quantum comb framework.
From: Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
Within this scheme, the channel for the k-th tooth \({{\mathcal{V}}}_{k}({\theta }_{k})\) is now parameterized by θk that remains tunable to adjustments during the optimization phase, and θ = (θ0, …, θm) is denoted as the vector of all parameters in this PQComb. a describes how the PQComb trains the protocol using the process-based loss function \({{\mathcal{L}}}_{p}\), which is computed by the average dissimilarity between the sampled output process \({\widehat{{\mathcal{N}}}}_{j,{\rm{out}}}({\boldsymbol{\theta }})\) and the expected process \({{\mathcal{N}}}_{j,{\rm{out}}}\). b describes how the PQComb trains the protocol using the comb-based loss function \({{\mathcal{L}}}_{c}\), which optimizes the Choi operator of the circuit CV(θ) using the performance operator Ω. Here each pair of two dots connected by a line represents the unnormalized maximally entangled state.
