Southwest Quantum Information and Technology

Transition Network Method for Stoquastic Heisenberg Hamiltonians

Presenting Author: Chaithanya Rayudu, University of New Mexico CQuIC
Contributing Author(s): Jun Takahashi, Cunlu Zhou

We consider the problem of finding the ground state energy of a Stoquastic Heisenberg Hamiltonian of the form \(H = \sum_{(i,j) \in E} -X_iX_j-Y_iY_j+Z_iZ_j\) on a graph \(G = (V,E)\). Stoquastic Hamiltonians are Hamiltonians with non-positive off diagonal elements in a particular known basis. The exact complexity of this problem is still unknown other than that it is in Stoq-MA. We present a rewriting of the problem as finding the highest eigen energy of a transition network which can yield insights into the structure of the problem, especially when symmetries are considered. We discuss the possibility of using this rewriting to develop a new Monto Carlo algorithm for (approximately) finding the ground state energy of classes of stoquastic Hamiltonians.

(Session 5 : Thursday from 5:00 pm - 7:00 pm)