Sumeet S, Hörmann M, Schmidt KP (2026)
Publication Type: Journal article
Publication year: 2026
Book Volume: 8
Article Number: 023358
Journal Issue: 2
DOI: 10.1103/sdpn-s42c
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.
APA:
Sumeet, S., Hörmann, M., & Schmidt, K.P. (2026). Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization. Physical Review Research, 8(2). https://doi.org/10.1103/sdpn-s42c
MLA:
Sumeet, Sumeet, Max Hörmann, and Kai Phillip Schmidt. "Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization." Physical Review Research 8.2 (2026).
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