Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries

• URL: http://arxiv.org/abs/2401.02355v1
• Date: Thu, 4 Jan 2024 16:53:47 GMT
• Title: Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Authors: Younes Javanmard, Ugne Liaubaite, Tobias J. Osborne, Xusheng Xu, Man-Hong Yung
• Abstract summary: We develop a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices.

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