## Recursive quantum algorithm to find the lowest eigenstate of a general Hamiltonian    [PDF]

Jeongho Bang, Seung-Woo Lee, Chang-Woo Lee, Hyunseok Jeong, Jinhyoung Lee
We propose a recursive quantum algorithm to find the lowest eigenstate of a general Hamiltonian. It yields the lowest eigenstate directly from an arbitrary chosen initial state without diagonalizing the Hamiltonian matrix. Remarkably, the effectiveness of the algorithm does not depend on any specific Hamiltonian structure as far as the initial state is not orthogonal to the lowest eigenstate. Further, our algorithm does not get trapped in the local-minima of the Hamiltonian. The number of recursions required for high accuracy $\simeq 1-\epsilon$ ($\epsilon \ll 1$) are bounded by the order of ${\cal O}((D\epsilon)^{-1})$, where $D$ is the difference between the two lowest eigenvalues.
View original: http://arxiv.org/abs/1212.6523