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Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization

Sumeet*, M. Hörmann, and K. P. Schmidt

  • *Contact author: sumeet.sumeet@fau.de
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Phys. Rev. Research 8, 023358 – Published 30 June, 2026

DOI: https://doi.org/10.1103/sdpn-s42c

Abstract

We propose a quantum algorithm for computing one-quasiparticle excitation energies in the thermodynamic limit by combining numerical linked-cluster expansions (NLCEs) and the variational quantum eigensolver (VQE). Our approach uses VQE to block diagonalize the cluster Hamiltonian through a single-unitary transformation. This unitary is then postprocessed using the projective cluster-additive transformation (PCAT) to ensure cluster additivity, a key requirement for NLCE convergence. We benchmark our method on the transverse-field Ising model (TFIM) in one and two dimensions, and with longitudinal field, computing one-quasiparticle dispersions in the high-field polarized phase. We compare two cost function classes, trace minimization and variance based, demonstrating their effectiveness with the Hamiltonian variational ansatz (HVA). For pure TFIM, ⌈N/2⌉ layers of HVA suffice: NLCE+VQE matches exact diagonalization. For TFIM with longitudinal field, where parity symmetry breaks and PCAT becomes essential, both ⌈N/2⌉ and N layers of HVA converge with increasing cluster size, with N layers providing improved accuracy. Our results establish PCAT as a cluster-additive framework that extends variational quantum algorithms to excited-state calculations in the thermodynamic limit via NLCE. While demonstrated with VQE, the PCAT postprocessing approach, which requires only low-energy eigenspace information, applies to any quantum eigenstate preparation method.

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Phys. Rev. Research 8, 023358– Published 30 June, 2026
  • Received 17 December 2025
  • Accepted 29 May 2026
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