2025/11/10 by Sumeet, Hörmann, M., Schmidt, K. P. · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2511.06623
openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
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, \lceil N/2 \rceil layers of HVA suffice: NLCE+VQE matches exact diagonalization. For TFIM with longitudinal field, where parity symmetry breaks and PCAT becomes essential, both \lceil N/2 \rceil 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.