openfermion.circuits.error_bound

Numerically upper bound the error in the ground state energy for the second order Trotter-Suzuki expansion.

openfermion.circuits.error_bound(
    terms, tight=False
)

terms a list of single-term QubitOperators in the Hamiltonian to be simulated.
tight whether to use the triangle inequality to give a loose upper bound on the error (default) or to calculate the norm of the error operator.

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

Notes: follows Poulin et al.'s work in "The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chemistry". In particular, Equation 16 is used for a loose upper bound, and the norm of Equation 9 is calculated for a tighter bound using the error operator from error_operator.

   Possible extensions of this function would be to get the
   expectation value of the error operator with the Hartree-Fock
   state or CISD state, which can scalably bound the error in
   the ground state but much more accurately than the triangle
   inequality.