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  • Letter
  • Open Access

Imaginary time spectral transforms for excited-state preparation

D. A. Millar1,2,*, L. W. Anderson1, E. Altamura3,4, O. Wallis3, M. E. Sahin3, J. Crain5,6, and S. J. Thomson1,7,†

  • *Contact author: declan.millar@ibm.com
  • †Contact author: steven.thomson@ed.ac.uk
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Phys. Rev. Research 8, L022042 – Published 3 June, 2026

DOI: https://doi.org/10.1103/v4rc-gmcx

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 midspectrum 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.

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Phys. Rev. Research 8, L022042– Published 3 June, 2026
  • Received 8 August 2025
  • Accepted 3 May 2026
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