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We report numerical results on the diagonalization of 1D transverse fieldIsing model. Numerical simulations using the Pauli product representation yielddiagonalization from 3 spins to 22 spins in the transverse field Ising modelwith the number of global Jacobi unitary transformations and number of finalterms in diagonalized spin z representation both grew polynomial with thenumber of spins. These results computed on a classical computer show promise inconstructing a quantum circuit to simulate diagonalized generic many-particleHamiltonians using polynomial number of gates.

Polynomial Scaling of Numerical Diagonalization of the 1D Transverse Field Ising Model into a Commuting Basis using the Pauli Product Representation