Quantum algorithms for Schrieffer-Wolff transformation

• URL: http://arxiv.org/abs/2201.13304v1
• Date: Mon, 31 Jan 2022 15:27:57 GMT
• Title: Quantum algorithms for Schrieffer-Wolff transformation
• Authors: Zongkang Zhang, Yongdan Yang, Xiaosi Xu, Ying Li
• Abstract summary: The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems. It describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of unperturbed Hamiltonian. This unitary transformation can be realized by quantum circuits.
• Score: 4.237239130164727
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of unperturbed Hamiltonian. This unitary transformation decoupling the low-energy and high-energy subspaces for the transformed Hamiltonian can be realized by quantum circuits. We give a fully quantum algorithm for realizing the SW transformation. We also propose a hybrid quantum-classical algorithm for finding the effective Hamiltonian on NISQ hardware, where a general cost function is used to indicate the decoupling degree. Numerical simulations without or with noise and experiments on quantum computer ibmq_manila are implemented for a Heisenberg chain model. Our results verify the algorithm and show its validity on near-term quantum computers.

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