openfermion.circuits.trotter_steps_required

Determine the number of Trotter steps for accurate energy estimation.

openfermion.circuits.trotter_steps_required(
    trotter_error_bound, time, energy_precision
)

This function calculates the number of steps required to bound the systematic energy shift (eigenvalue shift) of the effective Hamiltonian to a given precision. This is appropriate for applications like Quantum Phase Estimation (QPE) where we only care about the eigenvalues of the propagator. See appendix B from https://arxiv.org/pdf/1312.1695 This uses the following definition of error for time t and number of steps r:

\[ \lvert E - E^{TS} \rvert = \frac{t^2}{r^2} E_{bound}(H) \]

trotter_error_bound float

Upper bound on Trotter error in the state of interest.

time float

The total simulation time.

energy_precision float

Acceptable shift in state energy.

The integer minimum number of Trotter steps required.