Imaginary Time Spectral Transforms for Excited State Preparation

Abstract:Excited states of many-body quantum systems play a key role in a wide range of physical and chemical phenomena. Despite this, there is a notable lack of scalable algorithms capable of preparing highly excited eigenstates. To address this challenge, we introduce a general approach that directly targets eigenstates near a chosen energy, applicable to both classical and quantum simulation frameworks. Our approach combines the shift-invert mechanism with imaginary time evolution, enabling the construction of excited states of large many-body quantum systems. We demonstrate the technique classically by computing mid-spectrum eigenstates of disordered spin chains with up to $L=128$ sites. Based on this, we propose a hybrid scheme compatible with near-term quantum hardware.

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)

arXiv:2508.00065 [quant-ph]

(or arXiv:2508.00065v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2508.00065 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. Research 8, L022042 (2026)

https://doi.org/10.1103/v4rc-gmcx Focus to learn more DOI(s) linking to related resources

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