Efficient Decomposition of Tridiagonal Matrices for Quantum Hamiltonian Simulation

An efficient procedure is presented for representing a tridiagonal matrix in the Pauli basis, allowing the construction of a Hamiltonian evolution circuit without the use of oracles. The method systematically determines all Pauli strings present in the decomposition and divides them into commuting subsets, with the efficiency in the number of commuting subsets being O(n).