Give terms simulated in a single stagger of a Trotter step.

Groups terms into hopping (i^ j + j^ i) and number (i^j^ i j + c_i i^ i + c_j j^ j) operators. Pre-computes term information (indices each operator acts on, as well as whether each operator is a hopping operator).

hamiltonian FermionOperator

The Hamiltonian.

input_ordering list

The initial Jordan-Wigner canonical order.

parity boolean

Whether to determine the terms from the next even (False = 0) or odd (True = 1) stagger.

external_potential_at_end bool

Whether to include the rotations from the external potential at the end of the Trotter step, or intersperse them throughout it.

A 3-tuple of terms from the Hamiltonian that are simulated in the stagger, the indices they act on, and whether they are hopping operators (all in the same order).

The "staggers" used here are the left (parity=False) and right (parity=True) staggers detailed in Kivlichan et al., "Quantum Simulation of Electronic Structure with Linear Depth and Connectivity", arxiv:1711.04789. As such, the Hamiltonian must be in the form discussed in that paper. This constrains it to have only hopping terms (i^ j + j^ i) and potential terms which are products of at most two number operators (n_i or n_i n_j).