Fig. 15: Tensor networks to compute the elements of the transformation matrices that are applied to the blocks of \({{\bf{H}}}^{{\prime} }\) and \({{\bf{S}}}^{{\prime} }\) during the single-site optimizations. | npj Quantum Information

Fig. 15: Tensor networks to compute the elements of the transformation matrices that are applied to the blocks of \({{\bf{H}}}^{{\prime} }\) and \({{\bf{S}}}^{{\prime} }\) during the single-site optimizations.

From: A quantum eigenvalue solver based on tensor networks

Fig. 15: Tensor networks to compute the elements of the transformation matrices that are applied to the blocks of $${{\bf{H}}}^{{\prime} }$$ H ′ and $${{\bf{S}}}^{{\prime} }$$ S ′ during the single-site optimizations.

a A tensor network to compute the elements of the d2χ2 × d2χ2 block transformation matrices {G[j]} corresponding to the local orbital rotation updates \(\hat{g}(\theta )\) in the basis of the two-site one-hot states of reference state j. b A tensor network to compute the elements of the dχ2 × d2χ2 isometries {T[j]} that, when applied to the blocks of the two-site expanded subspace matrices \({{\bf{H}}}^{{\prime} }\) and \({{\bf{S}}}^{{\prime} }\) (dim. Md2χ2), yield the blocks of the single-site expanded subspace matrices (dim. Mdχ2) (see Supplementary Note A.4 for a detailed explanation).

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