openfermion.circuits.split_operator_trotter_error_operator_diagonal_two_body

Compute the split-operator Trotter error of a diagonal two-body

Hamiltonian.

hamiltonian (FermionOperator): The diagonal Coulomb Hamiltonian to compute the Trotter error for. order (str): Whether to simulate the split-operator Trotter step with the kinetic energy T first (order='T+V') or with the potential energy V first (order='V+T').

error_operator The second-order Trotter error operator.

Notes:

The second-order split-operator Trotter error is calculated from the double commutator [T, [V, T]] + [V, [V, T]] / 2 when T is simulated before V (i.e. exp(-iTt/2) exp(-iVt) exp(-iTt/2)), and from the double commutator [V, [T, V]] + [T, [T, V]] / 2 when V is simulated before T, following Equation 9 of "The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chemistry" by Poulin et al. The Trotter error operator is then obtained by dividing by 12.