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

• URL: http://arxiv.org/abs/2511.06623v1
• Date: Mon, 10 Nov 2025 02:02:07 GMT
• Title: Quantum algorithm for one quasi-particle excitations in the thermodynamic limit via cluster-additive block-diagonalization
• Authors: Sumeet, M. Hörmann, K. P. Schmidt,
• Abstract summary: We propose a quantum algorithm for computing one quasi-particle excitation energies in the thermodynamic limit by combining numerical linked-cluster expansions (NLCEs) and the variational quantum eigensolver (VQE)<n>Our results establish PCAT as a cluster-additive framework that extends variational quantum algorithms to excited-state calculations in the thermodynamic limit via NLCE.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a quantum algorithm for computing one quasi-particle 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 post-processed 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 quasi-particle 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 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 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 post-processing approach, which requires only low-energy eigenspace information, applies to any quantum eigenstate preparation method.

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