def time_evolution(
hamiltonian: QubitOperator,
time: Union[float, sympy.Expr],
method: str = "Trotter",
trotter_order: int = 1,
) -> circuits.Circuit:
"""Create a circuit simulating evolution under given Hamiltonian.
Args:
hamiltonian: The Hamiltonian to be evolved under.
time: Time duration of the evolution.
method: Time evolution method. Currently the only option is 'Trotter'.
trotter_order: order of Trotter evolution (1 by default).
Returns:
Circuit approximating evolution under `hamiltonian`.
Circuit's unitary i approximately equal to exp(-i * time * hamiltonian).
"""
if method != "Trotter":
raise ValueError(f"Currently the method {method} is not supported.")
terms: Iterable = list(hamiltonian.get_operators())
return reduce(
operator.add,
(time_evolution_for_term(term, time / trotter_order)
for _index_order in range(trotter_order) for term in terms),
)
def time_evolution_derivatives(
hamiltonian: QubitOperator,
time: float,
method: str = "Trotter",
trotter_order: int = 1,
) -> Tuple[List[circuits.Circuit], List[float]]:
"""Generates derivative circuits for the time evolution operator defined in
function time_evolution
Args:
hamiltonian: The Hamiltonian to be evolved under. It should contain numeric
coefficients, symbolic expressions aren't supported.
time: time duration of the evolution.
method: time evolution method. Currently the only option is 'Trotter'.
trotter_order: order of Trotter evolution
Returns:
A Circuit simulating time evolution.
"""
if method != "Trotter":
raise ValueError(f"The method {method} is currently not supported.")
single_trotter_derivatives = []
factors = [1.0, -1.0]
output_factors = []
terms: Iterable = list(hamiltonian.get_operators())
for i, term_1 in enumerate(terms):
for factor in factors:
output = circuits.Circuit()
try:
if isinstance(term_1, QubitOperator):
r = list(term_1.terms.values())[0] / trotter_order
else:
r = complex(term_1.coefficient).real / trotter_order
except TypeError:
raise ValueError("Term coefficients need to be numerical. "
f"Offending term: {term_1}")
output_factors.append(r * factor)
shift = factor * (np.pi / (4.0 * r))
for j, term_2 in enumerate(terms):
output += time_evolution_for_term(
term_2,
(time + shift) / trotter_order if i == j else time /
trotter_order,
)
single_trotter_derivatives.append(output)
if trotter_order > 1:
output_circuits = []
final_factors = []
repeated_circuit = time_evolution(hamiltonian,
time,
method="Trotter",
trotter_order=1)
for position in range(trotter_order):
for factor, different_circuit in zip(output_factors,
single_trotter_derivatives):
output_circuits.append(
_generate_circuit_sequence(repeated_circuit,
different_circuit,
trotter_order, position))
final_factors.append(factor)
return output_circuits, final_factors
else:
return single_trotter_derivatives, output_factors
