def _fermion_term_to_majorana_operator(term: tuple) -> MajoranaOperator:
"""
Convert single terms of FermionOperator to Majorana.
(Auxiliary function of get_majorana_operator.)
Convention: even + odd indexing of Majorana modes derived from a
fermionic mode:
fermion annhil. c_k -> ( gamma_{2k} + 1.j * gamma_{2k+1} ) / 2
fermion creation c^_k -> ( gamma_{2k} - 1.j * gamma_{2k+1} ) / 2
Args:
term (tuple): single FermionOperator term.
Returns:
converted_term: single MajoranaOperator term.
Raises:
TypeError: if term is a tuple.
"""
if not isinstance(term, tuple):
raise TypeError('Term does not have the correct Type.')
converted_term = MajoranaOperator(())
for index, action in term:
converted_op = MajoranaOperator((2 * index, ), 0.5)
if action:
converted_op += MajoranaOperator((2 * index + 1, ), -0.5j)
else:
converted_op += MajoranaOperator((2 * index + 1, ), 0.5j)
converted_term *= converted_op
return converted_term
def test_majorana_operator_pow():
a = MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator((1, 2, 7), -0.5)
assert (a**2).terms == {(): -2.5, (0, 2, 5, 7): -1.5}
with pytest.raises(TypeError):
_ = a**-1
with pytest.raises(TypeError):
_ = a**'a'
def test_get_fermion_operator_majorana_operator():
a = MajoranaOperator((0, 3), 2.0) + MajoranaOperator((1, 2, 3))
op = get_fermion_operator(a)
expected_op = (-2j * (FermionOperator(((0, 0), (1, 0))) - FermionOperator(
((0, 0), (1, 1))) + FermionOperator(
((0, 1), (1, 0))) - FermionOperator(
((0, 1), (1, 1)))) - 2 * FermionOperator(
((0, 0), (1, 1), (1, 0))) + 2 * FermionOperator(
((0, 1), (1, 1), (1, 0))) + FermionOperator(
(0, 0)) - FermionOperator((0, 1)))
assert normal_ordered(op) == normal_ordered(expected_op)
def test_majorana_operator_init():
op = MajoranaOperator((0, 7, 4, 1, 10))
assert op.terms == {(0, 1, 4, 7, 10): -1.0}
op = MajoranaOperator((0, 1, 0, 1, 0))
assert op.terms == {(0, ): -1.0}
op = MajoranaOperator((3, 2, 5, 1, 3, 4))
assert op.terms == {(1, 2, 4, 5): 1.0}
op = MajoranaOperator((5, 10, 4, 3, 6, 9, 6))
assert op.terms == {(3, 4, 5, 9, 10): -1.0}
def test_majorana_operator_divide():
a = MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator((1, 2, 7), -0.5)
assert (a / 2).terms == {(0, 1, 5): 0.75, (1, 2, 7): -0.25}
a /= 2
assert a.terms == {(0, 1, 5): 0.75, (1, 2, 7): -0.25}
with pytest.raises(TypeError):
_ = a / 'a'
with pytest.raises(TypeError):
a /= 'a'
def test_majorana_operator_str():
zero = MajoranaOperator()
one = MajoranaOperator(())
still_zero = MajoranaOperator((0, 1, 5), 0.0)
a = MajoranaOperator((0, 1, 5), 1.5)
b = MajoranaOperator((1, 2, 7), -0.5)
assert str(zero) == '0'
assert str(one) == '1.0 ()'
assert str(still_zero) == '0'
assert str(a) == '1.5 (0, 1, 5)'
assert str(b) == '-0.5 (1, 2, 7)'
assert str(a + b) == """1.5 (0, 1, 5) +
def test_get_majorana_operator_fermion_operator(self):
"""Test conversion FermionOperator to MajoranaOperator."""
fermion_op = (-2j * (FermionOperator(
((0, 0), (1, 0))) - FermionOperator(
((0, 0), (1, 1))) + FermionOperator(
((0, 1), (1, 0))) - FermionOperator(
((0, 1), (1, 1)))) - 2 * FermionOperator(
((0, 0), (1, 1), (1, 0))) + 2 * FermionOperator(
((0, 1), (1, 1), (1, 0))) + FermionOperator(
(0, 0)) - FermionOperator((0, 1)))
majorana_op = get_majorana_operator(fermion_op)
expected_op = (MajoranaOperator((0, 3), 2.0) + MajoranaOperator(
(1, 2, 3)))
self.assertTrue(majorana_op == expected_op)
def _fermion_operator_to_majorana_operator(
fermion_operator: FermionOperator) -> MajoranaOperator:
"""
Convert FermionOperator to MajoranaOperator.
Auxiliar function of get_majorana_operator.
Args:
fermion_operator (FermionOperator): To convert to MajoranaOperator.
Returns:
majorana_operator object.
Raises:
TypeError: if input is not a FermionOperator.
"""
if not isinstance(fermion_operator, FermionOperator):
raise TypeError('Input a FermionOperator.')
majorana_operator = MajoranaOperator()
for term, coeff in fermion_operator.terms.items():
converted_term = _fermion_term_to_majorana_operator(term)
converted_term *= coeff
majorana_operator += converted_term
return majorana_operator
def setUp(self):
self.n_qubits = 5
self.majorana_operator = MajoranaOperator((1, 4, 9))
self.fermion_term = FermionOperator('1^ 2^ 3 4', -3.17)
self.fermion_operator = self.fermion_term + hermitian_conjugated(
self.fermion_term)
self.qubit_operator = jordan_wigner(self.fermion_operator)
self.interaction_operator = get_interaction_operator(
self.fermion_operator)
def test_bk_n_qubits_too_small(self):
with self.assertRaises(ValueError):
bravyi_kitaev(FermionOperator('2^ 3^ 5 0'), n_qubits=4)
with self.assertRaises(ValueError):
bravyi_kitaev(MajoranaOperator((2, 3, 9, 0)), n_qubits=4)
with self.assertRaises(ValueError):
bravyi_kitaev(get_interaction_operator(
FermionOperator('2^ 3^ 5 0')),
n_qubits=4)
def test_majorana_operator_add_subtract():
a = MajoranaOperator((0, 2, 3), -1.25)
b = MajoranaOperator((0, 2, 3), -0.5)
c = MajoranaOperator((1, 5, 7), 4.75)
d = MajoranaOperator((3, 5, 7), 2.25)
a += c
assert a.terms == {(0, 2, 3): -1.25, (1, 5, 7): 4.75}
a -= d
assert a.terms == {(0, 2, 3): -1.25, (1, 5, 7): 4.75, (3, 5, 7): 2.25}
a += MajoranaOperator((0, 2, 3), 0.5)
assert a.terms == {(0, 2, 3): -.75, (1, 5, 7): 4.75, (3, 5, 7): 2.25}
a -= MajoranaOperator((0, 2, 3), 0.25)
assert a.terms == {(0, 2, 3): -1.0, (1, 5, 7): 4.75, (3, 5, 7): 2.25}
assert (a + b).terms == {(0, 2, 3): -1.5, (1, 5, 7): 4.75, (3, 5, 7): 2.25}
assert (a - b).terms == {(0, 2, 3): -0.5, (1, 5, 7): 4.75, (3, 5, 7): 2.25}
with pytest.raises(TypeError):
_ = a + 0
with pytest.raises(TypeError):
a += 0
with pytest.raises(TypeError):
_ = a - 0
with pytest.raises(TypeError):
a -= 0
def test_majorana_operator_multiply():
a = MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator((1, 2, 7), -0.5)
b = MajoranaOperator((2, 3, 4), 1.75) - MajoranaOperator((0, 3, 6), 0.25)
assert (a * a).terms == {(): -2.5, (0, 2, 5, 7): -1.5}
assert (a * b).terms == {
(1, 3, 4, 7): 0.875,
(0, 1, 2, 3, 6, 7): -0.125,
(1, 3, 5, 6): 0.375,
(0, 1, 2, 3, 4, 5): -2.625
}
assert (2 * a).terms == (a * 2).terms == {(0, 1, 5): 3.0, (1, 2, 7): -1.0}
a *= 2
a *= MajoranaOperator(())
assert a.terms == {(0, 1, 5): 3.0, (1, 2, 7): -1.0}
with pytest.raises(TypeError):
_ = a * 'a'
with pytest.raises(TypeError):
_ = 'a' * a
with pytest.raises(TypeError):
a *= 'a'
def test_majorana_operator_repr():
a = MajoranaOperator((0, 1, 5), 1.5)
assert repr(a) == 'MajoranaOperator.from_dict(terms={(0, 1, 5): 1.5})'
def test_jordan_wigner_majorana_op_consistent():
op = (MajoranaOperator((1, 3, 4), 0.5) + MajoranaOperator(
(3, 7, 8, 9, 10, 12), 1.8) + MajoranaOperator((0, 4)))
assert jordan_wigner(op) == jordan_wigner(get_fermion_operator(op))
def test_bravyi_kitaev_majorana_op_consistent():
op = (MajoranaOperator((1, 3, 4), 0.5) + MajoranaOperator(
(3, 7, 8, 9, 10, 12), 1.8) + MajoranaOperator((0, 4)))
assert bravyi_kitaev(op) == bravyi_kitaev(get_fermion_operator(op))
def test_majorana_operator_neg():
a = MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator((1, 2, 7), -0.5)
assert (-a).terms == {(0, 1, 5): -1.5, (1, 2, 7): 0.5}
def test_majorana_operator_with_basis_rotated_by():
H = numpy.array([[1, 1], [1, -1]]) / numpy.sqrt(2)
a = MajoranaOperator((0, 1), 2.0)
op = a.with_basis_rotated_by(H)
assert op == MajoranaOperator.from_dict({(0, 1): -2.0})
b = MajoranaOperator((0, ), 2.0)
op = b.with_basis_rotated_by(H)
assert op == MajoranaOperator.from_dict({
(0, ): numpy.sqrt(2),
(1, ): numpy.sqrt(2)
})
c = MajoranaOperator((1, ), 2.0)
op = c.with_basis_rotated_by(H)
assert op == MajoranaOperator.from_dict({
(0, ): numpy.sqrt(2),
(1, ): -numpy.sqrt(2)
})
P = numpy.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]])
d = MajoranaOperator((0, 1, 2)) + MajoranaOperator((1, 2))
op = d.with_basis_rotated_by(P)
assert op == MajoranaOperator.from_dict({(0, 1, 2): 1.0, (0, 1): 1.0})
with pytest.raises(ValueError):
_ = a.with_basis_rotated_by(2 * H)
def test_majorana_operator_commutes_with():
a = MajoranaOperator((0, 1, 5))
b = MajoranaOperator((1, 2, 7))
c = MajoranaOperator((2, 3, 4))
d = MajoranaOperator((0, 3, 6))
assert a.commutes_with(b)
assert not a.commutes_with(c)
assert a.commutes_with(d)
assert b.commutes_with(c)
assert not b.commutes_with(d)
assert c.commutes_with(d)
assert (a + c).commutes_with(b + d)
e = MajoranaOperator((0, 1, 1, 1, 4, 5))
f = MajoranaOperator((0, 1, 1, 4))
assert e.commutes_with(f)
with pytest.raises(TypeError):
_ = e.commutes_with(0)
def test_majorana_operator_eq():
a = MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator((1, 2, 7), -0.5)
b = (MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator(
(1, 2, 7), -0.5) + MajoranaOperator((3, 4, 5), 0.0))
c = (MajoranaOperator((0, 1, 5), 1.5) + MajoranaOperator(
(1, 2, 7), -0.5) + MajoranaOperator((3, 4, 5), 0.1))
d = MajoranaOperator((0, 1, 5), 1.75) + MajoranaOperator((1, 2, 7), -0.75)
e = MajoranaOperator((0, 1, 5), 1.5) - MajoranaOperator((0, 3, 6), 0.25)
assert a == b
assert a != c
assert a != d
assert a != e
assert a != 0