def test_init_raising_lowering_ops(self):
"""Test __init__ for +_i -_i pattern"""
with self.subTest("one reg"):
actual = SpinOp("+_0 -_0", spin=1, register_length=1)
expected = SpinOp([("X_0^2", 1), ("Y_0^2", 1), ("Z_0", 1)],
spin=1,
register_length=1)
self.assertSpinEqual(actual, expected)
with self.subTest("two reg"):
actual = SpinOp("+_1 -_1 +_0 -_0", spin=3 / 2, register_length=2)
expected = SpinOp(
[
("X_0^2 X_1^2", 1),
("X_0^2 Y_1^2", 1),
("X_0^2 Z_1", 1),
("Y_0^2 X_1^2", 1),
("Y_0^2 Y_1^2", 1),
("Y_0^2 Z_1", 1),
("Z_0 X_1^2", 1),
("Z_0 Y_1^2", 1),
("Z_0 Z_1", 1),
],
spin=3 / 2,
register_length=2,
)
self.assertSpinEqual(actual, expected)
def test_init_multiple_digits(self):
"""Test __init__ for sparse label with multiple digits"""
actual = SpinOp([("X_10^20", 1 + 2j), ("X_12^34", 56)],
Fraction(5, 2),
register_length=13)
desired = [("X_10^20", 1 + 2j), ("X_12^34", 56)]
self.assertListEqual(actual.to_list(), desired)
def test_init_label(self, label, pre_processing):
"""Test __init__"""
spin = SpinOp(pre_processing(label), register_length=len(label) // 3)
expected_label = " ".join(lb for lb in label.split() if lb[0] != "I")
if not expected_label:
expected_label = f"I_{len(label) // 3 - 1}"
self.assertListEqual(spin.to_list(), [(expected_label, 1)])
self.assertSpinEqual(eval(repr(spin)), spin) # pylint: disable=eval-used
def test_add(self):
"""Test __add__"""
with self.subTest("sum of heisenberg"):
actual = self.heisenberg + self.heisenberg
desired = SpinOp(
(self.heisenberg_spin_array, 2 * self.heisenberg_coeffs),
spin=1)
self.assertSpinEqual(actual, desired)
with self.subTest("raising operator"):
plus = SpinOp("+", 3 / 2)
x = SpinOp("X", 3 / 2)
y = SpinOp("Y", 3 / 2)
self.assertSpinEqual(x + 1j * y, plus)
def test_equiv(self):
"""test equiv"""
op1 = SpinOp("+ZXY") + SpinOp("-XXX")
op2 = SpinOp("+ZXY")
op3 = SpinOp("+ZXY") + (1 + 1e-7) * SpinOp("-XXX")
self.assertFalse(op1.equiv(op2))
self.assertFalse(op1.equiv(op3))
self.assertTrue(op1.equiv(op3, atol=1e-6))
def test_flatten_ladder_ops(self):
"""Test _flatten_ladder_ops"""
actual = SpinOp._flatten_ladder_ops([("+-", 2j)])
self.assertSetEqual(
frozenset(actual),
frozenset([("XX", 2j), ("XY", 2), ("YX", -2), ("YY", 2j)]),
)
def second_q_ops(self, display_format: Optional[str] = None) -> SpinOp:
"""Return the Hamiltonian of the Ising model in terms of `SpinOp`.
Args:
display_format: Not supported for Spin operators. If specified, it will be ignored.
Returns:
SpinOp: The Hamiltonian of the Ising model.
"""
if display_format is not None:
logger.warning(
"Spin operators do not support display-format. Provided display-format "
"parameter will be ignored."
)
ham = []
weighted_edge_list = self._lattice.weighted_edge_list
register_length = self._lattice.num_nodes
# kinetic terms
for node_a, node_b, weight in weighted_edge_list:
if node_a == node_b:
index = node_a
ham.append((f"X_{index}", weight))
else:
index_left = node_a
index_right = node_b
coupling_parameter = weight
ham.append((f"Z_{index_left} Z_{index_right}", coupling_parameter))
return SpinOp(ham, spin=Fraction(1, 2), register_length=register_length)
def test_adjoint(self):
"""Test adjoint method"""
with self.subTest("heisenberg adjoint"):
actual = self.heisenberg.adjoint()
desired = SpinOp(
(self.heisenberg_spin_array,
self.heisenberg_coeffs.conjugate().T),
spin=1,
)
self.assertSpinEqual(actual, desired)
with self.subTest("imag heisenberg adjoint"):
actual = ~((3 + 2j) * self.heisenberg)
desired = SpinOp(
(
self.heisenberg_spin_array,
((3 + 2j) * self.heisenberg_coeffs).conjugate().T,
),
spin=1,
)
self.assertSpinEqual(actual, desired)
def test_init_heisenberg(self):
"""Test __init__ for Heisenberg model."""
actual = SpinOp(
[
("XX", -1),
("YY", -1),
("ZZ", -1),
("ZI", -0.3),
("IZ", -0.3),
],
spin=1,
)
self.assertSpinEqual(actual, self.heisenberg)
def map(self, second_q_op: SpinOp) -> PauliSumOp:
"""Map spins to qubits using the Logarithmic encoding.
Args:
second_q_op: Spins mapped to qubits.
Returns:
Qubit operators generated by the Logarithmic encoding
"""
qubit_ops_list: List[PauliSumOp] = []
# get logarithmic encoding of the general spin matrices.
spinx, spiny, spinz, identity = self._logarithmic_encoding(
second_q_op.spin)
for idx, (_, coeff) in enumerate(second_q_op.to_list()):
operatorlist: List[PauliSumOp] = []
for n_x, n_y, n_z in zip(second_q_op.x[idx], second_q_op.y[idx],
second_q_op.z[idx]):
operator_on_spin_i: List[PauliSumOp] = []
if n_x > 0:
operator_on_spin_i.append(
reduce(operator.matmul, [spinx] * int(n_x)))
if n_y > 0:
operator_on_spin_i.append(
reduce(operator.matmul, [spiny] * int(n_y)))
if n_z > 0:
operator_on_spin_i.append(
reduce(operator.matmul, [spinz] * int(n_z)))
if operator_on_spin_i:
single_operator_on_spin_i = reduce(operator.matmul,
operator_on_spin_i)
operatorlist.append(single_operator_on_spin_i)
else:
# If n_x=n_y=n_z=0, simply add the embedded Identity operator.
operatorlist.append(identity)
# Now, we can tensor all operators in this list
qubit_ops_list.append(coeff *
reduce(operator.xor, reversed(operatorlist)))
qubit_op = reduce(operator.add, qubit_ops_list)
return qubit_op
def setUp(self):
super().setUp()
self.heisenberg_spin_array = np.array([
[[1, 1], [0, 0], [0, 0], [0, 0], [0, 0]],
[[0, 0], [1, 1], [0, 0], [0, 0], [0, 0]],
[[0, 0], [0, 0], [1, 1], [1, 0], [0, 1]],
], )
self.heisenberg_coeffs = np.array([-1, -1, -1, -0.3, -0.3])
self.heisenberg = SpinOp(
(self.heisenberg_spin_array, self.heisenberg_coeffs),
spin=1,
)
self.zero_op = SpinOp(
(np.array([[[0, 0]], [[0, 0]], [[0, 0]]]), np.array([0])),
spin=1,
)
self.spin_1_matrix = {
"I": np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]),
"X": np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]]) / np.sqrt(2),
"Y":
np.array([[0, -1j, 0], [1j, 0, -1j], [0, 1j, 0]]) / np.sqrt(2),
"Z": np.array([[1, 0, 0], [0, 0, 0], [0, 0, -1]]),
}
def test_simplify(self):
"""Test simplify"""
with self.subTest("trivial reduce"):
actual = (self.heisenberg - self.heisenberg).simplify()
self.assertListEqual(actual.to_list(), [("I_1", 0)])
with self.subTest("nontrivial reduce"):
test_op = SpinOp(
(
np.array([[[0, 1], [0, 1]], [[0, 0], [0, 0]],
[[1, 0], [1, 0]]]),
np.array([1.5, 2.5]),
),
spin=3 / 2,
)
actual = test_op.simplify()
self.assertListEqual(actual.to_list(), [("Z_0 X_1", 4)])
with self.subTest("nontrivial reduce 2"):
test_op = SpinOp(
(
np.array([
[[0, 1], [0, 1], [1, 1]],
[[0, 0], [0, 0], [0, 0]],
[[1, 0], [1, 0], [0, 0]],
]),
np.array([1.5, 2.5, 2]),
),
spin=3 / 2,
)
actual = test_op.simplify()
self.assertListEqual(actual.to_list(), [("Z_0 X_1", 4),
("X_0 X_1", 2)])
with self.subTest("nontrivial reduce 3"):
test_op = SpinOp([("+_0 -_0", 1)], register_length=4)
actual = test_op.simplify()
self.assertListEqual(actual.to_list(), [("Z_0", 1), ("Y_0^2", 1),
("X_0^2", 1)])
class TestLinearMapper(QiskitNatureTestCase):
"""Test Linear Mapper"""
spin_op1 = SpinOp([("Y_0^2", -0.432 + 1.32j)], 0.5, 1)
ref_qubit_op1 = (-0.054 + 0.165j) * (I ^ I) + (0.054 - 0.165j) * (Z ^ Z)
spin_op2 = SpinOp([("X_0 Z_0 I_1", -1.139 + 0.083j)], 0.5, 2)
ref_qubit_op2 = (0.010375 + 0.142375j) * (I ^ I ^ Y ^ X) + (
-0.010375 - 0.142375j) * (I ^ I ^ X ^ Y)
spin_op3 = SpinOp([("X_0 Y_0^2 Z_0 X_1 Y_1 Y_2 Z_2", -0.18 + 1.204j)], 0.5,
3)
ref_qubit_op3 = (
(0.000587890625 + 8.7890625e-05j) * (Y ^ Y ^ I ^ Z ^ Y ^ X) +
(0.000587890625 + 8.7890625e-05j) * (X ^ X ^ I ^ Z ^ Y ^ X) +
(-0.000587890625 - 8.7890625e-05j) * (Y ^ Y ^ Z ^ I ^ Y ^ X) +
(-0.000587890625 - 8.7890625e-05j) * (X ^ X ^ Z ^ I ^ Y ^ X) +
(-0.000587890625 - 8.7890625e-05j) * (Y ^ Y ^ I ^ Z ^ X ^ Y) +
(-0.000587890625 - 8.7890625e-05j) * (X ^ X ^ I ^ Z ^ X ^ Y) +
(0.000587890625 + 8.7890625e-05j) * (Y ^ Y ^ Z ^ I ^ X ^ Y) +
(0.000587890625 + 8.7890625e-05j) * (X ^ X ^ Z ^ I ^ X ^ Y))
spin_op4 = SpinOp([("I_0 Z_1", -0.875 - 0.075j)], 1.5, 2)
ref_qubit_op4 = ((-0.65625 - 0.05625j) * (Z ^ I ^ I ^ I ^ I ^ I ^ I ^ I) +
(-0.21875 - 0.01875j) * (I ^ Z ^ I ^ I ^ I ^ I ^ I ^ I) +
(0.21875 + 0.01875j) * (I ^ I ^ Z ^ I ^ I ^ I ^ I ^ I) +
(0.65625 + 0.05625j) * (I ^ I ^ I ^ Z ^ I ^ I ^ I ^ I))
spin_op5 = SpinOp(
[("X_0 I_1 I_2 I_3 I_4 I_5 I_6 I_7", 4 + 0j)], 0.5, 8) + SpinOp(
[("I_0^2 I_2 I_3 I_4 I_5 I_6 I_7 I_8", 8 + 0j)], 0.5, 8)
ref_qubit_op5 = (
(8.0 + 0j) *
(I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I) +
(1.0 + 0j) *
(I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ X ^ X) +
(1.0 + 0j) *
(I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ I ^ Y ^ Y))
@data(
(spin_op1, ref_qubit_op1),
(spin_op2, ref_qubit_op2),
(spin_op3, ref_qubit_op3),
(spin_op4, ref_qubit_op4),
(spin_op5, ref_qubit_op5),
)
@unpack
def test_mapping(self, spin_op, ref_qubit_op):
"""Test mapping to qubit operator"""
mapper = LinearMapper()
qubit_op = mapper.map(spin_op)
self.assertEqual(qubit_op, ref_qubit_op)
class TestLogarithmicMapper(QiskitNatureTestCase):
"""Test Logarithmic Mapper"""
spin_op1 = SpinOp([("Y_0", -0.432 + 1.32j)], 0.5, 1)
ref_qubit_op1 = (-0.216 + 0.66j) * (Y)
spin_op2 = SpinOp([("X_0 Z_0 I_1", -1.139 + 0.083j)], 0.5, 2)
ref_qubit_op2 = (0.02075 + 0.28475j) * (I ^ Y)
spin_op3 = SpinOp([("X_0 Y_0^2 Z_0 X_1 Y_1 Y_2 Z_2", -0.18 + 1.204j)], 0.5,
3)
ref_qubit_op3 = (-0.004703125 - 0.000703125j) * (X ^ Z ^ Y)
spin_op4 = SpinOp([("I_0 Z_1", -0.875 - 0.075j)], 1.5, 2)
ref_qubit_op4 = (-0.4375 - 0.0375j) * (I ^ Z ^ I ^ I) + (
-0.875 - 0.075j) * (Z ^ I ^ I ^ I)
spin_op5 = SpinOp(
[("X_0 I_1 I_2 I_3 I_4 I_5 I_6 I_7", 4 + 0j)], 0.5, 8) + SpinOp(
[("I_0^2 I_2 I_3 I_4 I_5 I_6 I_7 I_8", 8 + 0j)], 0.5, 8)
ref_qubit_op5 = (8.0 + 0j) * (I ^ I ^ I ^ I ^ I ^ I ^ I ^ I) + (
2.0 + 0j) * (I ^ I ^ I ^ I ^ I ^ I ^ I ^ X)
spin_op6 = SpinOp([("Z_0", -0.875 - 0.075j)], 1, 1)
ref_qubit_op6 = ((-0.4375 - 0.0375j) * (I ^ I) + (0.4375 + 0.0375j) *
(I ^ Z) + (-0.875 - 0.075j) * (Z ^ Z))
ref_qubit_op7 = ((-0.4375 - 0.0375j) * (I ^ I) + (-0.4375 - 0.0375j) *
(I ^ Z) + (-0.875 - 0.075j) * (Z ^ I))
@data(
(spin_op1, ref_qubit_op1),
(spin_op2, ref_qubit_op2),
(spin_op3, ref_qubit_op3),
(spin_op4, ref_qubit_op4),
(spin_op5, ref_qubit_op5),
(spin_op6, ref_qubit_op6, 2),
(spin_op6, ref_qubit_op7, 2, False),
)
@unpack
def test_mapping(self, spin_op, ref_qubit_op, padding=1, embed_upper=True):
"""Test mapping to qubit operator"""
mapper = LogarithmicMapper(padding, embed_upper)
qubit_op = mapper.map(spin_op)
self.assertEqual(qubit_op, ref_qubit_op)
def map(self, second_q_op: SpinOp) -> PauliSumOp:
qubit_ops_list: List[PauliSumOp] = []
# get linear encoding of the general spin matrices
spinx, spiny, spinz, identity = self._linear_encoding(second_q_op.spin)
for idx, (_, coeff) in enumerate(second_q_op.to_list()):
operatorlist: List[PauliSumOp] = []
for n_x, n_y, n_z in zip(second_q_op.x[idx], second_q_op.y[idx], second_q_op.z[idx]):
operator_on_spin_i: List[PauliSumOp] = []
if n_x > 0:
operator_on_spin_i.append(reduce(operator.matmul, [spinx] * int(n_x)))
if n_y > 0:
operator_on_spin_i.append(reduce(operator.matmul, [spiny] * int(n_y)))
if n_z > 0:
operator_on_spin_i.append(reduce(operator.matmul, [spinz] * int(n_z)))
if np.any([n_x, n_y, n_z]) > 0:
single_operator_on_spin_i = reduce(operator.matmul, operator_on_spin_i)
operatorlist.append(single_operator_on_spin_i.reduce())
else:
# If n_x=n_y=n_z=0, simply add the embedded Identity operator.
operatorlist.append(identity)
# Now, we can tensor all operators in this list
# NOTE: in Qiskit's opflow the `XOR` (i.e. `^`) operator does the tensor product
qubit_ops_list.append(coeff * reduce(operator.xor, reversed(operatorlist)))
qubit_op = reduce(operator.add, qubit_ops_list)
return qubit_op
def _logarithmic_encoding(
self, spin: Union[Fraction, int]
) -> Tuple[PauliSumOp, PauliSumOp, PauliSumOp, PauliSumOp]:
"""The logarithmic encoding.
Args:
spin: Positive half-integer (integer or half-odd-integer) that represents spin.
Returns:
A tuple containing four PauliSumOp.
"""
spin_op_encoding: List[PauliSumOp] = []
dspin = int(2 * spin + 1)
num_qubits = int(np.ceil(np.log2(dspin)))
# Get the spin matrices
spin_matrices = [
SpinOp(symbol, spin=spin).to_matrix() for symbol in "XYZ"
]
# Append the identity
spin_matrices.append(np.eye(dspin))
# Embed the spin matrices in a larger matrix of size 2**num_qubits x 2**num_qubits
embedded_spin_matrices = [
self._embed_matrix(matrix, num_qubits) for matrix in spin_matrices
]
# Generate operators from these embedded spin matrices
embedded_operators = [
Operator(matrix) for matrix in embedded_spin_matrices
]
for op in embedded_operators:
op = SparsePauliOp.from_operator(op)
op.chop()
spin_op_encoding.append(PauliSumOp(1.0 * op))
return tuple(spin_op_encoding) # type: ignore
def assertSpinEqual(first: SpinOp, second: SpinOp):
"""Fail if two SpinOps have different matrix representations."""
np.testing.assert_array_almost_equal(first.to_matrix(),
second.to_matrix())
def test_init_dense_label(self, labels, pre_processing):
"""Test __init__ for dense label"""
dense_label, sparse_label = labels
actual = SpinOp(pre_processing(dense_label))
desired = SpinOp([(sparse_label, 1)], register_length=len(dense_label))
self.assertSpinEqual(actual, desired)
class TestSpinOp(QiskitNatureTestCase):
"""SpinOp tests."""
def setUp(self):
super().setUp()
self.heisenberg_spin_array = np.array([
[[1, 1], [0, 0], [0, 0], [0, 0], [0, 0]],
[[0, 0], [1, 1], [0, 0], [0, 0], [0, 0]],
[[0, 0], [0, 0], [1, 1], [1, 0], [0, 1]],
], )
self.heisenberg_coeffs = np.array([-1, -1, -1, -0.3, -0.3])
self.heisenberg = SpinOp(
(self.heisenberg_spin_array, self.heisenberg_coeffs),
spin=1,
)
self.zero_op = SpinOp(
(np.array([[[0, 0]], [[0, 0]], [[0, 0]]]), np.array([0])),
spin=1,
)
self.spin_1_matrix = {
"I": np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]),
"X": np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]]) / np.sqrt(2),
"Y":
np.array([[0, -1j, 0], [1j, 0, -1j], [0, 1j, 0]]) / np.sqrt(2),
"Z": np.array([[1, 0, 0], [0, 0, 0], [0, 0, -1]]),
}
@staticmethod
def assertSpinEqual(first: SpinOp, second: SpinOp):
"""Fail if two SpinOps have different matrix representations."""
np.testing.assert_array_almost_equal(first.to_matrix(),
second.to_matrix())
@data(*product(
(*sparse_labels(1), *sparse_labels(2), *sparse_labels(3)),
(str2str, str2tuple, str2list),
))
@unpack
def test_init_label(self, label, pre_processing):
"""Test __init__"""
spin = SpinOp(pre_processing(label), register_length=len(label) // 3)
expected_label = " ".join(lb for lb in label.split() if lb[0] != "I")
if not expected_label:
expected_label = f"I_{len(label) // 3 - 1}"
self.assertListEqual(spin.to_list(), [(expected_label, 1)])
self.assertSpinEqual(eval(repr(spin)), spin) # pylint: disable=eval-used
@data(*product(
(
*zip(dense_labels(1), sparse_labels(1)),
*zip(dense_labels(2), sparse_labels(2)),
*zip(dense_labels(3), sparse_labels(3)),
),
(str2str, str2tuple, str2list),
))
@unpack
def test_init_dense_label(self, labels, pre_processing):
"""Test __init__ for dense label"""
dense_label, sparse_label = labels
actual = SpinOp(pre_processing(dense_label))
desired = SpinOp([(sparse_label, 1)], register_length=len(dense_label))
self.assertSpinEqual(actual, desired)
def test_init_pm_label(self):
"""Test __init__ with plus and minus label"""
with self.subTest("plus"):
plus = SpinOp([("+_0", 2)], register_length=1)
desired = SpinOp([("X_0", 2), ("Y_0", 2j)], register_length=1)
self.assertSpinEqual(plus, desired)
with self.subTest("dense plus"):
plus = SpinOp([("+", 2)])
desired = SpinOp([("X_0", 2), ("Y_0", 2j)], register_length=1)
self.assertSpinEqual(plus, desired)
with self.subTest("minus"):
minus = SpinOp([("-_0", 2)], register_length=1)
desired = SpinOp([("X_0", 2), ("Y_0", -2j)], register_length=1)
self.assertSpinEqual(minus, desired)
with self.subTest("minus"):
minus = SpinOp([("-", 2)])
desired = SpinOp([("X_0", 2), ("Y_0", -2j)], register_length=1)
self.assertSpinEqual(minus, desired)
with self.subTest("plus tensor minus"):
plus_tensor_minus = SpinOp([("+_0 -_1", 3)], register_length=2)
desired = SpinOp(
[("X_0 X_1", 3), ("Y_0 X_1", 3j), ("X_0 Y_1", -3j),
("Y_0 Y_1", 3)],
register_length=2,
)
self.assertSpinEqual(plus_tensor_minus, desired)
with self.subTest("dense plus tensor minus"):
plus_tensor_minus = SpinOp([("+-", 3)])
desired = SpinOp(
[("X_0 X_1", 3), ("Y_0 X_1", 3j), ("X_0 Y_1", -3j),
("Y_0 Y_1", 3)],
register_length=2,
)
self.assertSpinEqual(plus_tensor_minus, desired)
def test_init_heisenberg(self):
"""Test __init__ for Heisenberg model."""
actual = SpinOp(
[
("XX", -1),
("YY", -1),
("ZZ", -1),
("ZI", -0.3),
("IZ", -0.3),
],
spin=1,
)
self.assertSpinEqual(actual, self.heisenberg)
def test_init_multiple_digits(self):
"""Test __init__ for sparse label with multiple digits"""
actual = SpinOp([("X_10^20", 1 + 2j), ("X_12^34", 56)],
Fraction(5, 2),
register_length=13)
desired = [("X_10^20", 1 + 2j), ("X_12^34", 56)]
self.assertListEqual(actual.to_list(), desired)
@data("IJX", "Z_0 X_0", "Z_0 +_0", "+_0 X_0")
def test_init_invalid_label(self, label):
"""Test __init__ for invalid label"""
with self.assertRaises(ValueError):
SpinOp(label)
def test_init_raising_lowering_ops(self):
"""Test __init__ for +_i -_i pattern"""
with self.subTest("one reg"):
actual = SpinOp("+_0 -_0", spin=1, register_length=1)
expected = SpinOp([("X_0^2", 1), ("Y_0^2", 1), ("Z_0", 1)],
spin=1,
register_length=1)
self.assertSpinEqual(actual, expected)
with self.subTest("two reg"):
actual = SpinOp("+_1 -_1 +_0 -_0", spin=3 / 2, register_length=2)
expected = SpinOp(
[
("X_0^2 X_1^2", 1),
("X_0^2 Y_1^2", 1),
("X_0^2 Z_1", 1),
("Y_0^2 X_1^2", 1),
("Y_0^2 Y_1^2", 1),
("Y_0^2 Z_1", 1),
("Z_0 X_1^2", 1),
("Z_0 Y_1^2", 1),
("Z_0 Z_1", 1),
],
spin=3 / 2,
register_length=2,
)
self.assertSpinEqual(actual, expected)
def test_neg(self):
"""Test __neg__"""
actual = -self.heisenberg
desired = SpinOp((self.heisenberg_spin_array, -self.heisenberg_coeffs),
spin=1)
self.assertSpinEqual(actual, desired)
def test_mul(self):
"""Test __mul__, and __rmul__"""
actual = self.heisenberg * 2
desired = SpinOp(
(self.heisenberg_spin_array, 2 * self.heisenberg_coeffs), spin=1)
self.assertSpinEqual(actual, desired)
def test_div(self):
"""Test __truediv__"""
actual = self.heisenberg / 3
desired = SpinOp(
(self.heisenberg_spin_array, self.heisenberg_coeffs / 3), spin=1)
self.assertSpinEqual(actual, desired)
def test_add(self):
"""Test __add__"""
with self.subTest("sum of heisenberg"):
actual = self.heisenberg + self.heisenberg
desired = SpinOp(
(self.heisenberg_spin_array, 2 * self.heisenberg_coeffs),
spin=1)
self.assertSpinEqual(actual, desired)
with self.subTest("raising operator"):
plus = SpinOp("+", 3 / 2)
x = SpinOp("X", 3 / 2)
y = SpinOp("Y", 3 / 2)
self.assertSpinEqual(x + 1j * y, plus)
def test_sub(self):
"""Test __sub__"""
actual = self.heisenberg - self.heisenberg
self.assertSpinEqual(actual, self.zero_op)
def test_adjoint(self):
"""Test adjoint method"""
with self.subTest("heisenberg adjoint"):
actual = self.heisenberg.adjoint()
desired = SpinOp(
(self.heisenberg_spin_array,
self.heisenberg_coeffs.conjugate().T),
spin=1,
)
self.assertSpinEqual(actual, desired)
with self.subTest("imag heisenberg adjoint"):
actual = ~((3 + 2j) * self.heisenberg)
desired = SpinOp(
(
self.heisenberg_spin_array,
((3 + 2j) * self.heisenberg_coeffs).conjugate().T,
),
spin=1,
)
self.assertSpinEqual(actual, desired)
# TODO: implement adjoint for same register operators.
# with self.sub Test("adjoint same register op"):
# actual = SpinOp("X_0 Y_0 Z_0").adjoint()
# print(actual.to_matrix())
# print(SpinOp("X_0 Y_0 Z_0").to_matrix().T.conjugate())
def test_simplify(self):
"""Test simplify"""
with self.subTest("trivial reduce"):
actual = (self.heisenberg - self.heisenberg).simplify()
self.assertListEqual(actual.to_list(), [("I_1", 0)])
with self.subTest("nontrivial reduce"):
test_op = SpinOp(
(
np.array([[[0, 1], [0, 1]], [[0, 0], [0, 0]],
[[1, 0], [1, 0]]]),
np.array([1.5, 2.5]),
),
spin=3 / 2,
)
actual = test_op.simplify()
self.assertListEqual(actual.to_list(), [("Z_0 X_1", 4)])
with self.subTest("nontrivial reduce 2"):
test_op = SpinOp(
(
np.array([
[[0, 1], [0, 1], [1, 1]],
[[0, 0], [0, 0], [0, 0]],
[[1, 0], [1, 0], [0, 0]],
]),
np.array([1.5, 2.5, 2]),
),
spin=3 / 2,
)
actual = test_op.simplify()
self.assertListEqual(actual.to_list(), [("Z_0 X_1", 4),
("X_0 X_1", 2)])
with self.subTest("nontrivial reduce 3"):
test_op = SpinOp([("+_0 -_0", 1)], register_length=4)
actual = test_op.simplify()
self.assertListEqual(actual.to_list(), [("Z_0", 1), ("Y_0^2", 1),
("X_0^2", 1)])
@data(*dense_labels(1))
def test_to_matrix_single_qutrit(self, label):
"""Test to_matrix for single qutrit op"""
actual = SpinOp(label, 1).to_matrix()
np.testing.assert_array_almost_equal(actual, self.spin_1_matrix[label])
@data(*product(dense_labels(1), dense_labels(1)))
@unpack
def test_to_matrix_sum_single_qutrit(self, label1, label2):
"""Test to_matrix for sum qutrit op"""
actual = (SpinOp(label1, 1) + SpinOp(label2, 1)).to_matrix()
np.testing.assert_array_almost_equal(
actual, self.spin_1_matrix[label1] + self.spin_1_matrix[label2])
@data(*dense_labels(2))
def test_to_matrix_two_qutrit(self, label):
"""Test to_matrix for two qutrit op"""
actual = SpinOp(label, 1).to_matrix()
desired = np.kron(self.spin_1_matrix[label[0]],
self.spin_1_matrix[label[1]])
np.testing.assert_array_almost_equal(actual, desired)
@data(*dense_labels(1), *dense_labels(2), *dense_labels(3))
def test_consistency_with_pauli(self, label):
"""Test consistency with pauli"""
actual = SpinOp(label).to_matrix()
desired = Pauli(label).to_matrix() / (2**(len(label) -
label.count("I")))
np.testing.assert_array_almost_equal(actual, desired)
def test_flatten_ladder_ops(self):
"""Test _flatten_ladder_ops"""
actual = SpinOp._flatten_ladder_ops([("+-", 2j)])
self.assertSetEqual(
frozenset(actual),
frozenset([("XX", 2j), ("XY", 2), ("YX", -2), ("YY", 2j)]),
)
def test_hermiticity(self):
"""test is_hermitian"""
# deliberately define test operator with X and Y which creates duplicate terms in .to_list()
# in case .adjoint() simplifies terms
with self.subTest("operator hermitian"):
test_op = SpinOp("+ZXY") + SpinOp("-ZXY")
self.assertTrue(test_op.is_hermitian())
with self.subTest("operator not hermitian"):
test_op = SpinOp("+ZXY") - SpinOp("-ZXY")
self.assertFalse(test_op.is_hermitian())
with self.subTest("test passing atol"):
test_op = SpinOp("+ZXY") + (1 + 1e-7) * SpinOp("-ZXY")
self.assertFalse(test_op.is_hermitian())
self.assertFalse(test_op.is_hermitian(atol=1e-8))
self.assertTrue(test_op.is_hermitian(atol=1e-6))
def test_equiv(self):
"""test equiv"""
op1 = SpinOp("+ZXY") + SpinOp("-XXX")
op2 = SpinOp("+ZXY")
op3 = SpinOp("+ZXY") + (1 + 1e-7) * SpinOp("-XXX")
self.assertFalse(op1.equiv(op2))
self.assertFalse(op1.equiv(op3))
self.assertTrue(op1.equiv(op3, atol=1e-6))
def test_init_pm_label(self):
"""Test __init__ with plus and minus label"""
with self.subTest("plus"):
plus = SpinOp([("+_0", 2)], register_length=1)
desired = SpinOp([("X_0", 2), ("Y_0", 2j)], register_length=1)
self.assertSpinEqual(plus, desired)
with self.subTest("dense plus"):
plus = SpinOp([("+", 2)])
desired = SpinOp([("X_0", 2), ("Y_0", 2j)], register_length=1)
self.assertSpinEqual(plus, desired)
with self.subTest("minus"):
minus = SpinOp([("-_0", 2)], register_length=1)
desired = SpinOp([("X_0", 2), ("Y_0", -2j)], register_length=1)
self.assertSpinEqual(minus, desired)
with self.subTest("minus"):
minus = SpinOp([("-", 2)])
desired = SpinOp([("X_0", 2), ("Y_0", -2j)], register_length=1)
self.assertSpinEqual(minus, desired)
with self.subTest("plus tensor minus"):
plus_tensor_minus = SpinOp([("+_0 -_1", 3)], register_length=2)
desired = SpinOp(
[("X_0 X_1", 3), ("Y_0 X_1", 3j), ("X_0 Y_1", -3j),
("Y_0 Y_1", 3)],
register_length=2,
)
self.assertSpinEqual(plus_tensor_minus, desired)
with self.subTest("dense plus tensor minus"):
plus_tensor_minus = SpinOp([("+-", 3)])
desired = SpinOp(
[("X_0 X_1", 3), ("Y_0 X_1", 3j), ("X_0 Y_1", -3j),
("Y_0 Y_1", 3)],
register_length=2,
)
self.assertSpinEqual(plus_tensor_minus, desired)
def test_mul(self):
"""Test __mul__, and __rmul__"""
actual = self.heisenberg * 2
desired = SpinOp(
(self.heisenberg_spin_array, 2 * self.heisenberg_coeffs), spin=1)
self.assertSpinEqual(actual, desired)
def test_init_invalid_label(self, label):
"""Test __init__ for invalid label"""
with self.assertRaises(ValueError):
SpinOp(label)
def test_consistency_with_pauli(self, label):
"""Test consistency with pauli"""
actual = SpinOp(label).to_matrix()
desired = Pauli(label).to_matrix() / (2**(len(label) -
label.count("I")))
np.testing.assert_array_almost_equal(actual, desired)
def test_to_matrix_two_qutrit(self, label):
"""Test to_matrix for two qutrit op"""
actual = SpinOp(label, 1).to_matrix()
desired = np.kron(self.spin_1_matrix[label[0]],
self.spin_1_matrix[label[1]])
np.testing.assert_array_almost_equal(actual, desired)
def test_to_matrix_sum_single_qutrit(self, label1, label2):
"""Test to_matrix for sum qutrit op"""
actual = (SpinOp(label1, 1) + SpinOp(label2, 1)).to_matrix()
np.testing.assert_array_almost_equal(
actual, self.spin_1_matrix[label1] + self.spin_1_matrix[label2])
def test_to_matrix_single_qutrit(self, label):
"""Test to_matrix for single qutrit op"""
actual = SpinOp(label, 1).to_matrix()
np.testing.assert_array_almost_equal(actual, self.spin_1_matrix[label])
def test_neg(self):
"""Test __neg__"""
actual = -self.heisenberg
desired = SpinOp((self.heisenberg_spin_array, -self.heisenberg_coeffs),
spin=1)
self.assertSpinEqual(actual, desired)
def test_hermiticity(self):
"""test is_hermitian"""
# deliberately define test operator with X and Y which creates duplicate terms in .to_list()
# in case .adjoint() simplifies terms
with self.subTest("operator hermitian"):
test_op = SpinOp("+ZXY") + SpinOp("-ZXY")
self.assertTrue(test_op.is_hermitian())
with self.subTest("operator not hermitian"):
test_op = SpinOp("+ZXY") - SpinOp("-ZXY")
self.assertFalse(test_op.is_hermitian())
with self.subTest("test passing atol"):
test_op = SpinOp("+ZXY") + (1 + 1e-7) * SpinOp("-ZXY")
self.assertFalse(test_op.is_hermitian())
self.assertFalse(test_op.is_hermitian(atol=1e-8))
self.assertTrue(test_op.is_hermitian(atol=1e-6))
def _linear_encoding(self, spin: Union[Fraction, float]) -> List[PauliSumOp]:
"""
Generates a 'linear_encoding' of the spin S operators 'X', 'Y', 'Z' and 'identity'
to qubit operators (linear combinations of pauli strings).
In this 'linear_encoding' each individual spin S system is represented via
2S+1 qubits and the state |s> is mapped to the state |00...010..00>, where the s-th qubit is
in state 1.
Returns:
The 4-element list of transformed spin S 'X', 'Y', 'Z' and 'identity' operators.
I.e. spin_op_encoding[0]` corresponds to the linear combination of pauli strings needed
to represent the embedded 'X' operator
"""
spin_op_encoding: List[PauliSumOp] = []
dspin = int(2 * spin + 1)
nqubits = dspin
# quick functions to generate a pauli with X / Y / Z at location `i`
pauli_id = Pauli("I" * nqubits)
def pauli_x(i):
return Pauli("I" * i + "X" + "I" * (nqubits - i - 1))
def pauli_y(i):
return Pauli("I" * i + "Y" + "I" * (nqubits - i - 1))
def pauli_z(i):
return Pauli("I" * i + "Z" + "I" * (nqubits - i - 1))
# 1. build the non-diagonal X operator
x_summands = []
for i, coeff in enumerate(np.diag(SpinOp("X", spin=spin).to_matrix(), 1)):
x_summands.append(
PauliSumOp(
coeff / 2.0 * SparsePauliOp(pauli_x(i).dot(pauli_x(i + 1)))
+ coeff / 2.0 * SparsePauliOp(pauli_y(i).dot(pauli_y(i + 1)))
)
)
spin_op_encoding.append(reduce(operator.add, x_summands))
# 2. build the non-diagonal Y operator
y_summands = []
for i, coeff in enumerate(np.diag(SpinOp("Y", spin=spin).to_matrix(), 1)):
y_summands.append(
PauliSumOp(
-1j * coeff / 2.0 * SparsePauliOp(pauli_x(i).dot(pauli_y(i + 1)))
+ 1j * coeff / 2.0 * SparsePauliOp(pauli_y(i).dot(pauli_x(i + 1)))
)
)
spin_op_encoding.append(reduce(operator.add, y_summands))
# 3. build the diagonal Z
z_summands = []
for i, coeff in enumerate(np.diag(SpinOp("Z", spin=spin).to_matrix())):
# get the first upper diagonal of coeff.
z_summands.append(
PauliSumOp(
coeff / 2.0 * SparsePauliOp(pauli_z(i)) + coeff / 2.0 * SparsePauliOp(pauli_id)
)
)
z_operator = reduce(operator.add, z_summands)
spin_op_encoding.append(z_operator)
# 4. add the identity operator
spin_op_encoding.append(PauliSumOp(1.0 * SparsePauliOp(pauli_id)))
# return the lookup table for the transformed XYZI operators
return spin_op_encoding
def test_div(self):
"""Test __truediv__"""
actual = self.heisenberg / 3
desired = SpinOp(
(self.heisenberg_spin_array, self.heisenberg_coeffs / 3), spin=1)
self.assertSpinEqual(actual, desired)