Detecting quasi-degenerate ground states in 1D topological models via VQE

• URL: http://arxiv.org/abs/2408.15179v2
• Date: Thu, 29 Aug 2024 12:28:37 GMT
• Title: Detecting quasi-degenerate ground states in 1D topological models via VQE
• Authors: Carola Ciaramelletti, Martin Beseda, Mirko Consiglio, Luca Lepori, Tony J. G. Apollaro, Simone Paganelli,
• Abstract summary: We study the exact ground states of the Su--Schrieffer--Heeger open chain and of the Kitaev open chain. These models host symmetry-protected topological phases, characterized by edge modes with vanishing single-particle energy in the thermodynamic limit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the exact ground states of the Su--Schrieffer--Heeger open chain and of the Kitaev open chain, using the Variational Quantum Eigensolver (VQE) algorithm. These models host symmetry-protected topological phases, characterized by edge modes with vanishing single-particle energy in the thermodynamic limit. The same fact prevents the standard VQE algorithm from converging to the correct ground state for finite chains, since it is quasi-degenerate in energy with other many-body states. Notably, this quasi-degeneracy cannot be removed by small perturbations, as in typical spin systems. We address this issue by imposing appropriate constraints on the VQE evolution and constructing appropriate variational circuits, to restrict the probed portion of the Hilbert space along the same evolution. These constraints stem from both general properties of the topological phases and of the studied Hamiltonians. In this way, the improved VQE algorithm achieves an accurate convergence to the exact ground states in each phase. The present approach promises large applicability, also to realistic systems and possibly with different topology, thanks to the very high fidelity achieved also on systems with a relatively high number of qubits.

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