Extended Data Fig. 3: Noise susceptibility and eigenstate overlaps.

(a) Density-of-states for a spin-1 AFM chain, computed from a polarized reference state \(\left\vert S\right\rangle ={\left\vert 0\right\rangle }^{\otimes N}\) (top), and ground state reference \(\left\vert S\right\rangle =\left\vert GS\right\rangle\) (bottom). The spectrum is separated into sectors distinguished by their operator weight from \(\left\vert S\right\rangle\). For the polarized state, these correspond to sectors with well-defined S^z. For the ground-state, each sector is orthogonalized with respect to lower-weight sectors. Each sector is phenomenologically broadened by \({e}^{-\gamma t{n}_{{\rm{flips}}}}\) to simulate the operator-weight dependence of decoherence. When computing low-energy properties, the ground-state reference is more robust to noise, since the low-energy eigenstates can be reached with lower-weight operators. (b) The amplitude of the corresponding spectral peak is determined by the eigenstate overlap. We analyze the ground-state overlap for an AFM spin-1 chain performing DMRG for low bond dimensions (D = 1, 2) and find that it is much larger for bond-dimension D = 2 matrix product states (red diamonds) compared to bond-dimension D = 1, that is,mean-field states (green circles). Interestingly, the ground state overlap decays slower with the chain length for D = 2 indicating that the fidelity density is large. This feature makes low bond dimension states a promising direction for efficient state preparation within our scheme since they can efficiently be decomposed into short circuits.