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  • Open Access

Quantum algorithms for Schrieffer-Wolff transformation

Zongkang Zhang, Yongdan Yang, Xiaosi Xu*, and Ying Li†

  • Graduate School of China Academy of Engineering Physics, Beijing 100193, China

  • *xsxu@gscaep.ac.cn
  • †yli@gscaep.ac.cn
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Phys. Rev. Research 4, 043023 – Published 12 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043023

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 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.

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Phys. Rev. Research 4, 043023– Published 12 October, 2022
  • Received 14 February 2022
  • Accepted 6 September 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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