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openfermion.circuits.low_depth_second_order_trotter_error_bound

Numerically upper bound the error in the ground state energy

openfermion.circuits.low_depth_second_order_trotter_error_bound(
    terms,
    indices=None,
    is_hopping_operator=None,
    jellium_only=False,
    verbose=False
)

for the second-order Trotter-Suzuki expansion.

terms a list of single-term FermionOperators in the Hamiltonian to be simulated.
indices a set of indices the terms act on in the same order as terms.
is_hopping_operator a list of whether each term is a hopping operator.
jellium_only Whether the terms are from the jellium Hamiltonian only, rather than the full dual basis Hamiltonian (i.e. whether c_i = c for all number operators i^ i, or whether they depend on i as is possible in the general case).
verbose Whether to print percentage progress.

A float upper bound on norm of error in the ground state energy.

Notes:

Follows Equation 9 of Poulin et al.'s work in "The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chemistry" to calculate the error operator, for the "stagger"-based Trotter step for detailed in Kivlichan et al., "Quantum Simulation of Electronic Structure with Linear Depth and Connectivity", arxiv:1711.04789.