Scientists have developed a new method for extracting excitation spectra from complex many-electron systems, improving spectral reconstruction accuracy despite limitations in current quantum hardware resolution and environmental noise. Taichi Kosugi and colleagues at Quemix Inc, in collaboration with MITSUI KINZOKU COMPANY, National Institutes for Quantum Science and Technology (QST), The University of Tokyo, and Quantum Materials and Applications Research Centre, present QPE averaged over variable grids, or QAVG, which combines low-resolution quantum phase estimation with multiple origin shifts and continuous parametrization. They accurately determined the spectra of a CO molecule adsorbed onto a $χ$-Fe$_$5C$_2$ surface using Quantinuum H2-2, employing both physical and logical quantum phase estimation circuits with Steane code and offline bit-flip correction. QAVG effectively suppresses local minima during optimisation and offers a strong pathway towards quantum simulations of correlated spectra, enabling advancements in the field as fault-tolerant quantum computers develop. Variable grid averaging enhances quantum spectral reconstruction for molecular modelling Deviations in spectral reconstruction were reduced to less than the nominal QPE resolution, representing a two-fold improvement over previous methods and enabling accurate analysis previously impossible with limited quantum hardware. This breakthrough stemmed from employing a new technique, QPE averaged over variable grids, or QAVG, which combines multiple low-resolution measurements to overcome limitations imposed by noise and grid resolution in quantum computers. The fundamental principle behind QAVG lies in its ability to mitigate the effects of spectral leakage, a common artefact in Fourier-transform based spectroscopy where energy from a given spectral feature spreads into adjacent frequencies. Traditional quantum phase estimation (QPE) relies on accurately determining the eigenvalues of the system’s Hamiltonian, which requires a finely discretised grid of energy levels. However, current noisy intermediate-scale quantum (NISQ) devices struggle to maintain the coherence necessary for high-resolution QPE. QAVG circumvents this by performing multiple QPE measurements with slightly shifted energy