$σ$-VQE: Excited-state preparation of quantum many-body scars with shallow circuits

• URL: http://arxiv.org/abs/2602.20881v1
• Date: Tue, 24 Feb 2026 13:21:04 GMT
• Title: $σ$-VQE: Excited-state preparation of quantum many-body scars with shallow circuits
• Abstract summary: We present and benchmark a type of variational quantum eigensolver (VQE)<n>It is designed to target mid-spectrum eigenstates and prepare quantum many-body scar states.<n>A proof-of-principle demonstration using a small-system instance was carried out on IBM Fez.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present and benchmark a type of variational quantum eigensolver (VQE), which we denote the $σ$-VQE. It is designed to target mid-spectrum eigenstates and prepare quantum many-body scar states. The approach leverages the fact that noisy intermediate-scale quantum devices are limited in their ability to generate generic highly-entangled states. This modified VQE pairs a low-depth circuit with an energy-selective objective that explicitly penalizes energy variance around a chosen target energy. The cost function exploits the limited expressibility of the shallow circuit as atypical low-entanglement eigenstates such as scar states are preferentially selected. We validate this mechanism across two complementary families of models that contain many-body scar states: the Shiraishi-Mori embedding approach, and the matrix-product state parent Hamiltonian construction. We define an unbiased estimation scheme for the nonlinear cost function that is compatible with qubit-wise commuting grouping and bitstring reuse. A proof-of-principle demonstration using a small-system instance was carried out on IBM Fez (Heron r2 QPU). These results motivate its use both as a practical "scar detector" and as a state-preparation primitive for initializing nonthermal eigenstate-supported dynamics.

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