def test_moments_with_shots() -> None:
b = BraketBackend(local=True)
c = Circuit(1).H(0)
z = QubitPauliString(Qubit(0), Pauli.Z)
e = b.get_pauli_expectation_value(c, z, n_shots=10)
assert abs(e) <= 1
v = b.get_pauli_variance(c, z, n_shots=10)
assert v <= 1
op = QubitPauliOperator({z: 3})
e = b.get_operator_expectation_value(c, op, n_shots=10)
assert abs(e) <= 3
v = b.get_operator_variance(c, op, n_shots=10)
assert v <= 9
def test_variance() -> None:
b = BraketBackend(local=True)
assert b.supports_variance
# - Prepare a state (1/sqrt(2), 1/sqrt(2)).
# - Measure w.r.t. the operator Z which has evcs (1,0) (evl=+1) and (0,1) (evl=-1).
# - Get +1 with prob. 1/2 and -1 with prob. 1/2.
c = Circuit(1).H(0)
z = QubitPauliString(Qubit(0), Pauli.Z)
assert b.get_pauli_expectation_value(c, z) == pytest.approx(0)
assert b.get_pauli_variance(c, z) == pytest.approx(1)
op = QubitPauliOperator({z: 3})
assert b.get_operator_expectation_value(c, op) == pytest.approx(0)
assert b.get_operator_variance(c, op) == pytest.approx(9)