Quantum algorithms for Schrieffer-Wolff transformation

作     者：Zongkang Zhang Yongdan Yang Xiaosi Xu Ying Li 

作者机构：Graduate School of China Academy of Engineering Physics Beijing 100193 China 

出 版 物：《Physical Review Research》 (Phys. Rev. Res.)

年 卷 期：2022年第4卷第4期

页      面：043023-043023页

核心收录：

基　　金：National Natural Science Foundation of China, NSFC, (11875050, 12088101) National Safety Academic Fund, NSAF, (U1930403) 

主　　题：Quantum algorithms Quantum computation 

摘      要：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 an 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.