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      Quantum algorithms for Schrieffer-Wolff transformation

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          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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          Author and article information

          Journal
          31 January 2022
          Article
          2201.13304
          4800a369-e17a-42f0-ac44-48bbe3dc25a7

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          11 pages, 5 figures
          quant-ph

          Quantum physics & Field theory
          Quantum physics & Field theory

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