  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.
