Thermodynamic-limit dispersion relations on trapped-ion quantum hardware

• URL: http://arxiv.org/abs/2605.28599v1
• Date: Wed, 27 May 2026 15:16:30 GMT
• Title: Thermodynamic-limit dispersion relations on trapped-ion quantum hardware
• Abstract summary: We run a numerical linked-cluster expansion with a quantum algorithm (NLCE+QA)<n>For the quantum algorithm, we consider adiabatic state preparation (ASP), as well as a variational quantum eigensolver (VQE) trained on a classical device.<n>The final expectation values are obtained from the QPU, using a novel alternative to the Hadamard test that we name the CX-test.
• Score: 1.5006258585503878
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We run a numerical linked-cluster expansion with a quantum algorithm (NLCE+QA), computing ground-state energies and one quasi-particle dispersions in the thermodynamic limit using a 20-qubit trapped-ion quantum processing unit (QPU). The NLCE+QA framework extracts thermodynamic-limit properties from small-cluster calculations, making it naturally suited for near-term quantum devices. Projector-based block-diagonalization schemes such as projective cluster-additive transformation (PCAT) are essential to NLCE+QA, and they involve matrix inversion and square root operations that amplify measurement noise. A central question is therefore whether current hardware can provide expectation values that are accurate enough to withstand non-linear classical post-processing. We explore this challenge for the transverse-field Ising model (TFIM) in one dimension, on a ladder geometry, as well as in a longitudinal field in one dimension. For the quantum algorithm, we consider adiabatic state preparation (ASP), as well as a variational quantum eigensolver (VQE) trained on a classical device. The final expectation values are obtained from the QPU, using a novel alternative to the Hadamard test that we name the CX-test. We explore the regimes currently attainable on quantum devices and comment on the improvements needed for quantum computers to achieve results beyond classical reach.

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