Fig. 7: Tensor network contractions for the evaluation of the cost function.
From: Realization of quantum signal processing on a noisy quantum computer
a Contraction of \({{{\rm{Tr}}}}({\tilde{{{{\mathcal{W}}}}}}^{{\dagger} }\tilde{{{{\mathcal{W}}}}})\) for \(\tilde{{{{\mathcal{W}}}}}\) of Fig. 5a. b Contraction of \({{{\rm{Tr}}}}({\tilde{{{{\mathcal{W}}}}}}^{{\dagger} }\tilde{H})\) for \(\tilde{{{{\mathcal{W}}}}}\) of Fig. 5a and \(\tilde{H}\) represented by a matrix product operator. Note that the terms in the gradient (34) and Hessian (35) can be evaluated using similar tensor network contractions.
