qat.fermion.trotterisation.make_trotterisation_routine

qat.fermion.trotterisation.make_trotterisation_routine(hamiltonian: SpinHamiltonian | FermionHamiltonian | ElectronicStructureHamiltonian, n_trotter_steps: int, final_time: float | None = 1.0, method: str | None = 'jordan-wigner') → QRoutine

This function first trotterizes the evolution operator $e^{- i H t}$ of a Hamiltonian $H$ using a first order approximation. If the Hamiltonian is fermionic, it is converted to its spin representation.

Parameters:

hamiltonian (Union[SpinHamiltonian, FermionHamiltonian, ElectronicStructureHamiltonian]) – Hamiltonian to trotterize.
n_trotter_steps (int) – Number $n$ of Trotter steps.
final_time (Optional[float]) – Time $t$ in the evolution operator.
method (Optional[str]) – Method to use for the transformation to a spin representation. Other available methods include "bravyi-kitaev" and "parity". Defaults to "jordan-wigner".

Returns:

Gates to apply to perform the time evolution of the chemical Hamiltonian with trotterisation.

Return type:

QRoutine

Notes

In the fermionic case :

$e^{- i H t} \approx \prod_{k = 1}^{n} (\prod_{p q} e^{- i \frac{t}{n} h_{p q} c_{p}^{†} c_{q}} \prod_{p q r s} e^{- \frac{i}{2} \frac{t}{n} h_{p q r s} e^{- i c_{p}^{†} c_{q}^{†} c_{r} c_{s}}})$

This operator is then mapped to a product of Pauli operators via a Jordan-Wigner transformation and the resulting QRoutine is returned.
The QRoutine implements a first order Trotter approximation, but higher order approximations are possible.