Mohammad H. Amin, Anatly Yu. Smirnov, Neil G. Dickson, Marshal Drew-Brook
An approximate diagonalization method is proposed that combines exact
diagonalization and perturbation expansion to calculate low energy eigenvalues
and eigenfunctions of a Hamiltonian. The method involves deriving an effective
Hamiltonian for each eigenvalue to be calculated, using perturbation expansion,
and extracting the eigenvalue from the diagonalization of the effective
Hamiltonian. The size of the effective Hamiltonian can be significantly smaller
than that of the original Hamiltonian, hence the diagonalization can be done
much faster. We compare the results of our method with those obtained using
exact diagonalization and quantum Monte Carlo calculation for random problem
instances with up to 128 qubits.
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http://arxiv.org/abs/1202.2817
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