Give terms from the Fermi-Hubbard Hamiltonian in simulated order.

Uses the simulation ordering, grouping terms into hopping (i^ j + j^ i) and on-site potential (i^j^ i j) operators. Pre-computes term information (indices each operator acts on, as well as whether each operator is a hopping operator).

hubbard_hamiltonian FermionOperator

The Hamiltonian.

original_ordering list

The initial Jordan-Wigner canonical order.

A 3-tuple of terms from the Hubbard Hamiltonian in order of simulation, the indices they act on, and whether they are hopping operators (both also in the same order).

Assumes that the Hubbard model has spin and is on a 2D square aperiodic lattice. Uses the "stagger"-based Trotter step for the Hubbard model detailed in Kivlichan et al., "Quantum Simulation of Electronic Structure with Linear Depth and Connectivity", arxiv:1711.04789.