def test_PauliRot_decomposition_XY(self):
"""Test that the decomposition for a XY rotation is correct."""
theta = 0.4
op = qml.PauliRot(theta, "XY", wires=[0, 1])
decomp_ops = op.decomposition(theta, "XY", wires=[0, 1])
assert len(decomp_ops) == 5
assert decomp_ops[0].name == "Hadamard"
assert decomp_ops[0].wires == [0]
assert decomp_ops[1].name == "RX"
assert decomp_ops[1].wires == [1]
assert decomp_ops[1].params[0] == np.pi / 2
assert decomp_ops[2].name == "MultiRZ"
assert decomp_ops[2].wires == [0, 1]
assert decomp_ops[2].params[0] == theta
assert decomp_ops[3].name == "Hadamard"
assert decomp_ops[3].wires == [0]
assert decomp_ops[4].name == "RX"
assert decomp_ops[4].wires == [1]
assert decomp_ops[4].params[0] == -np.pi / 2
def expand(self):
with qml.tape.QuantumTape() as tape:
for i, pauli_word in enumerate(_state_preparation_pauli_words(len(self.wires))):
qml.PauliRot(self.parameters[0][i], pauli_word, wires=self.wires)
return tape
def ArbitraryUnitary(weights, wires):
"""Implements an arbitrary unitary on the specified wires.
An arbitrary unitary on :math:`n` wires is parametrized by :math:`4^n - 1`
independent real parameters. This templates uses Pauli word rotations to
parametrize the unitary.
**Example**
ArbitraryUnitary can be used as a building block, e.g. to parametrize arbitrary
two-qubit operations in a circuit:
.. code-block:: python
@qml.template
def arbitrary_nearest_neighbour_interaction(weights, wires):
qml.broadcast(unitary=ArbitraryUnitary, pattern="double", wires=wires, params=weights)
Args:
weights (tensor_like): The angles of the Pauli word rotations, needs to have length :math:`4^n - 1`
where :math:`n` is the number of wires the template acts upon.
wires (Iterable or Wires): Wires that the template acts on. Accepts an iterable of numbers or strings, or
a Wires object.
"""
wires = Wires(wires)
_preprocess(weights, wires)
for i, pauli_word in enumerate(_all_pauli_words_but_identity(len(wires))):
qml.PauliRot(weights[i], pauli_word, wires=wires)
def ArbitraryUnitary(weights, wires):
"""Implements an arbitrary unitary on the specified wires.
An arbitrary unitary on :math:`n` wires is parametrized by :math:`4^n - 1`
independent real parameters. This templates uses Pauli word rotations to
parametrize the unitary.
**Example**
ArbitraryUnitary can be used as a building block, e.g. to parametrize arbitrary
two-qubit operations in a circuit:
.. code-block:: python
@qml.template
def arbitrary_nearest_neighbour_interaction(weights, wires):
qml.broadcast(unitary=ArbitraryUnitary, pattern="double", wires=wires, params=weights)
Args:
weights (array[float]): The angles of the Pauli word rotations, needs to have length :math:`4^n - 1`
where :math:`n` is the number of wires the template acts upon.
wires (List[int]): The wires on which the arbitrary unitary acts.
"""
wires = check_wires(wires)
n_wires = len(wires)
expected_shape = (4 ** n_wires - 1,)
check_shape(
weights,
expected_shape,
msg="'weights' must be of shape {}; got {}." "".format(expected_shape, get_shape(weights)),
)
for i, pauli_word in enumerate(_all_pauli_words_but_identity(len(wires))):
qml.PauliRot(weights[i], pauli_word, wires=wires)
def test_PauliRot_decomposition_XIYZ(self):
"""Test that the decomposition for a XIYZ rotation is correct."""
theta = 0.4
op = qml.PauliRot(theta, "XIYZ", wires=[0, 1, 2, 3])
decomp_ops = op.decomposition(theta, "XIYZ", wires=[0, 1, 2, 3])
assert len(decomp_ops) == 5
assert decomp_ops[0].name == "Hadamard"
assert decomp_ops[0].wires == Wires([0])
assert decomp_ops[1].name == "RX"
assert decomp_ops[1].wires == Wires([2])
assert decomp_ops[1].data[0] == np.pi / 2
assert decomp_ops[2].name == "MultiRZ"
assert decomp_ops[2].wires == Wires([0, 2, 3])
assert decomp_ops[2].data[0] == theta
assert decomp_ops[3].name == "Hadamard"
assert decomp_ops[3].wires == Wires([0])
assert decomp_ops[4].name == "RX"
assert decomp_ops[4].wires == Wires([2])
assert decomp_ops[4].data[0] == -np.pi / 2
def test_multirz_generator(self, pauli_word):
"""Test that the generator of the MultiRZ gate is correct."""
op = qml.PauliRot(0.3, pauli_word, wires=range(len(pauli_word)))
gen = op.generator
if pauli_word[0] == 'I':
# this is the identity
expected_gen = qml.Identity(wires=0)
else:
expected_gen = getattr(
qml, 'Pauli{}'.format(pauli_word[0]))(wires=0)
for i, pauli in enumerate(pauli_word[1:]):
i += 1
if pauli == 'I':
expected_gen = expected_gen @ qml.Identity(
wires=i)
else:
expected_gen = expected_gen @ getattr(
qml, 'Pauli{}'.format(pauli))(wires=i)
expected_gen_mat = expected_gen.matrix
assert np.allclose(gen[0], expected_gen_mat)
assert gen[1] == -0.5
def ArbitraryStatePreparation(weights, wires):
"""Implements an arbitrary state preparation on the specified wires.
An arbitrary state on :math:`n` wires is parametrized by :math:`2^{n+1} - 2`
independent real parameters. This templates uses Pauli word rotations to
parametrize the unitary.
**Example**
ArbitraryStatePreparation can be used to train state preparations,
for example using a circuit with some measurement observable ``H``:
.. code-block:: python
dev = qml.device("default.qubit", wires=4)
@qml.qnode(dev)
def vqe(weights):
qml.ArbitraryStatePreparations(weights, wires=[0, 1, 2, 3])
return qml.expval(qml.Hermitian(H, wires=[0, 1, 2, 3]))
Args:
weights (tensor_like): The angles of the Pauli word rotations, needs to have length :math:`2^(n+1) - 2`
where :math:`n` is the number of wires the template acts upon.
wires (Iterable or Wires): Wires that the template acts on. Accepts an iterable of numbers or strings, or
a Wires object.
"""
wires = Wires(wires)
_preprocess(weights, wires)
for i, pauli_word in enumerate(_state_preparation_pauli_words(len(wires))):
qml.PauliRot(weights[i], pauli_word, wires=wires)
def algebra_commutator(tape, observables, lie_algebra_basis_names, nqubits):
"""Calculate the Riemannian gradient in the Lie algebra with the parameter shift rule
(see :meth:`LieAlgebraOptimizer.get_omegas`).
Args:
tape (.QuantumTape or .QNode): input circuit
observables (list[.Observable]): list of observables to be measured. Can be grouped.
lie_algebra_basis_names (list[str]): List of strings corresponding to valid Pauli words.
nqubits (int): the number of qubits.
Returns:
func: Function which accepts the same arguments as the QNode. When called, this
function will return the Lie algebra commutator.
"""
tapes_plus_total = []
tapes_min_total = []
for obs in observables:
for o in obs:
# create a list of tapes for the plus and minus shifted circuits
tapes_plus = [qml.tape.JacobianTape(p + "_p") for p in lie_algebra_basis_names]
tapes_min = [qml.tape.JacobianTape(p + "_m") for p in lie_algebra_basis_names]
# loop through all operations on the input tape
for op in tape.operations:
for t in tapes_plus + tapes_min:
with t:
qml.apply(op)
for i, t in enumerate(tapes_plus):
with t:
qml.PauliRot(
np.pi / 2,
lie_algebra_basis_names[i],
wires=list(range(nqubits)),
)
qml.expval(o)
for i, t in enumerate(tapes_min):
with t:
qml.PauliRot(
-np.pi / 2,
lie_algebra_basis_names[i],
wires=list(range(nqubits)),
)
qml.expval(o)
tapes_plus_total.extend(tapes_plus)
tapes_min_total.extend(tapes_min)
return tapes_plus_total + tapes_min_total, None
def test_PauliRot_decomposition_Identity(self):
"""Test that decomposing the all-identity Pauli has no effect."""
theta = 0.4
op = qml.PauliRot(theta, "II", wires=[0, 1])
decomp_ops = op.decomposition(theta, "II", wires=[0, 1])
assert len(decomp_ops) == 0
def test_init_incorrect_pauli_word_length_error(self, pauli_word, wires):
"""Test that __init__ throws an error if a Pauli word of wrong length is supplied."""
with pytest.raises(
ValueError,
match="The given Pauli word has length .*, length .* was expected for wires .*",
):
qml.PauliRot(0.3, pauli_word, wires=wires)
def qfunc():
qml.RZ(0.1, wires=0)
qml.Hadamard(wires=0)
# No rotation angles specified for PauliRot since it is a gate that
# in principle acts on an arbitrary number of wires.
qml.PauliRot(0.2, "X", wires=0)
qml.RZ(0.1, wires=0)
qml.Hadamard(wires=0)
def test_init_incorrect_pauli_word_error(self):
"""Test that __init__ throws an error if a wrong Pauli word is supplied."""
with pytest.raises(
ValueError,
match='The given Pauli word ".*" contains characters that are not allowed.'
" Allowed characters are I, X, Y and Z",
):
qml.PauliRot(0.3, "IXYZV", wires=[0, 1, 2, 3, 4])
def test_PauliRot_all_Identity(self):
"""Test handling of the all-identity Pauli."""
theta = 0.4
op = qml.PauliRot(theta, "II", wires=[0, 1])
decomp_ops = op.decomposition(theta, "II", wires=[0, 1])
assert np.allclose(op.eigvals, np.exp(-1j * theta / 2) * np.ones(4))
assert np.allclose(op.matrix / op.matrix[0, 0], np.eye(4))
assert len(decomp_ops) == 0
def test_PauliRot_decomposition_ZZ(self):
"""Test that the decomposition for a ZZ rotation is correct."""
theta = 0.4
op = qml.PauliRot(theta, "ZZ", wires=[0, 1])
decomp_ops = op.decomposition(theta, "ZZ", wires=[0, 1])
assert len(decomp_ops) == 1
assert decomp_ops[0].name == "MultiRZ"
assert decomp_ops[0].wires == [0, 1]
assert decomp_ops[0].params[0] == theta
def test_do_not_expand(self):
"""Test that a tape with single-parameter operations with
unitary generators and non-parametric operations is not touched."""
with qml.tape.JacobianTape() as tape:
qml.RX(0.2, wires=0)
qml.Hadamard(0)
qml.PauliRot(0.9, "XY", wires=[0, 1])
qml.SingleExcitationPlus(-1.2, wires=[1, 0])
new_tape = qml.transforms.expand_nonunitary_gen(tape)
assert tape.operations == new_tape.operations
def op(op_name):
ops_list = {
"RX": qml.RX(0.123, wires=0),
"RY": qml.RY(1.434, wires=0),
"RZ": qml.RZ(2.774, wires=0),
"S": qml.S(wires=0),
"SX": qml.SX(wires=0),
"T": qml.T(wires=0),
"CNOT": qml.CNOT(wires=[0, 1]),
"CZ": qml.CZ(wires=[0, 1]),
"CY": qml.CY(wires=[0, 1]),
"SWAP": qml.SWAP(wires=[0, 1]),
"ISWAP": qml.ISWAP(wires=[0, 1]),
"SISWAP": qml.SISWAP(wires=[0, 1]),
"SQISW": qml.SQISW(wires=[0, 1]),
"CSWAP": qml.CSWAP(wires=[0, 1, 2]),
"PauliRot": qml.PauliRot(0.123, "Y", wires=0),
"IsingXX": qml.IsingXX(0.123, wires=[0, 1]),
"IsingXY": qml.IsingXY(0.123, wires=[0, 1]),
"IsingYY": qml.IsingYY(0.123, wires=[0, 1]),
"IsingZZ": qml.IsingZZ(0.123, wires=[0, 1]),
"Identity": qml.Identity(wires=0),
"Rot": qml.Rot(0.123, 0.456, 0.789, wires=0),
"Toffoli": qml.Toffoli(wires=[0, 1, 2]),
"PhaseShift": qml.PhaseShift(2.133, wires=0),
"ControlledPhaseShift": qml.ControlledPhaseShift(1.777, wires=[0, 2]),
"CPhase": qml.CPhase(1.777, wires=[0, 2]),
"MultiRZ": qml.MultiRZ(0.112, wires=[1, 2, 3]),
"CRX": qml.CRX(0.836, wires=[2, 3]),
"CRY": qml.CRY(0.721, wires=[2, 3]),
"CRZ": qml.CRZ(0.554, wires=[2, 3]),
"Hadamard": qml.Hadamard(wires=0),
"PauliX": qml.PauliX(wires=0),
"PauliY": qml.PauliY(wires=0),
"PauliZ": qml.PauliZ(wires=0),
"CRot": qml.CRot(0.123, 0.456, 0.789, wires=[0, 1]),
"DiagonalQubitUnitary": qml.DiagonalQubitUnitary(np.array([1.0, 1.0j]), wires=1),
"ControlledQubitUnitary": qml.ControlledQubitUnitary(
np.eye(2) * 1j, wires=[0], control_wires=[2]
),
"MultiControlledX": qml.MultiControlledX(wires=(0, 1, 2), control_values="01"),
"SingleExcitation": qml.SingleExcitation(0.123, wires=[0, 3]),
"SingleExcitationPlus": qml.SingleExcitationPlus(0.123, wires=[0, 3]),
"SingleExcitationMinus": qml.SingleExcitationMinus(0.123, wires=[0, 3]),
"DoubleExcitation": qml.DoubleExcitation(0.123, wires=[0, 1, 2, 3]),
"DoubleExcitationPlus": qml.DoubleExcitationPlus(0.123, wires=[0, 1, 2, 3]),
"DoubleExcitationMinus": qml.DoubleExcitationMinus(0.123, wires=[0, 1, 2, 3]),
"QFT": qml.QFT(wires=0),
"QubitSum": qml.QubitSum(wires=[0, 1, 2]),
"QubitCarry": qml.QubitCarry(wires=[0, 1, 2, 3]),
"QubitUnitary": qml.QubitUnitary(np.eye(2) * 1j, wires=0),
}
return ops_list.get(op_name)
def circuit_decomposed(weights):
qml.PauliRot(weights[0], "XI", wires=[0, 1])
qml.PauliRot(weights[1], "YI", wires=[0, 1])
qml.PauliRot(weights[2], "IX", wires=[0, 1])
qml.PauliRot(weights[3], "IY", wires=[0, 1])
qml.PauliRot(weights[4], "XX", wires=[0, 1])
qml.PauliRot(weights[5], "XY", wires=[0, 1])
return qml.expval(qml.PauliZ(0))
def test_PauliRot_wire_as_int(self):
"""Test that passing a single wire as an integer works."""
theta = 0.4
op = qml.PauliRot(theta, "Z", wires=0)
decomp_ops = op.decomposition(theta, "Z", wires=0)
assert np.allclose(op.eigvals, np.array([np.exp(-1j * theta / 2), np.exp(1j * theta / 2)]))
assert np.allclose(op.matrix, np.diag([np.exp(-1j * theta / 2), np.exp(1j * theta / 2)]))
assert len(decomp_ops) == 1
assert decomp_ops[0].name == "MultiRZ"
assert decomp_ops[0].wires == Wires([0])
assert decomp_ops[0].data[0] == theta
def ArbitraryStatePreparation(weights, wires):
"""Implements an arbitrary state preparation on the specified wires.
An arbitrary state on :math:`n` wires is parametrized by :math:`2^{n+1} - 2`
independent real parameters. This templates uses Pauli word rotations to
parametrize the unitary.
**Example**
ArbitraryStatePreparation can be used to train state preparations,
for example using a circuit with some measurement observable ``H``:
.. code-block:: python
dev = qml.device("default.qubit", wires=4)
@qml.qnode(dev)
def vqe(weights):
qml.ArbitraryStatePreparations(weights, wires=[0, 1, 2, 3])
return qml.expval(qml.Hermitian(H, wires=[0, 1, 2, 3]))
Args:
weights (array[float]): The angles of the Pauli word rotations, needs to have length :math:`2^(n+1) - 2`
where :math:`n` is the number of wires the template acts upon.
wires (Iterable or Wires): Wires that the template acts on. Accepts an iterable of numbers or strings, or
a Wires object.
"""
wires = Wires(wires)
n_wires = len(wires)
expected_shape = (2**(n_wires + 1) - 2, )
check_shape(
weights,
expected_shape,
msg="'weights' must be of shape {}; got {}."
"".format(expected_shape, get_shape(weights)),
)
wires = wires.tolist() # Todo: remove when ops take Wires object
for i, pauli_word in enumerate(_state_preparation_pauli_words(len(wires))):
qml.PauliRot(weights[i], pauli_word, wires=wires)
class TestApproxTimeEvolution:
"""Tests for the ApproxTimeEvolution template from the pennylane.templates.subroutine module."""
def test_hamiltonian_error(self):
"""Tests if the correct error is thrown when hamiltonian is not a pennylane.Hamiltonian object"""
n_wires = 2
dev = qml.device("default.qubit", wires=n_wires)
hamiltonian = np.array([[1, 1], [1, 1]])
@qml.qnode(dev)
def circuit():
ApproxTimeEvolution(hamiltonian, 2, 3)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]
with pytest.raises(ValueError, match="hamiltonian must be of type pennylane.Hamiltonian"):
circuit()
def test_n_error(self):
"""Tests if the correct error is thrown when n is not an integer"""
n_wires = 2
dev = qml.device("default.qubit", wires=n_wires)
hamiltonian = qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)])
n = 1.37
@qml.qnode(dev)
def circuit():
ApproxTimeEvolution(hamiltonian, 2, n)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]
with pytest.raises(ValueError, match="n must be of type int"):
circuit()
@pytest.mark.parametrize(
("hamiltonian", "output"),
[
(qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.Hadamard(0)]), "Hadamard"),
(
qml.Hamiltonian(
[1, 1],
[qml.PauliX(0) @ qml.Hermitian(np.array([[1, 1], [1, 1]]), 1), qml.PauliX(0)],
),
"Hermitian",
),
],
)
def test_non_pauli_error(self, hamiltonian, output):
"""Tests if the correct errors are thrown when the user attempts to input a matrix with non-Pauli terms"""
n_wires = 2
dev = qml.device("default.qubit", wires=n_wires)
@qml.qnode(dev)
def circuit():
ApproxTimeEvolution(hamiltonian, 2, 3)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]
with pytest.raises(
ValueError, match="hamiltonian must be written in terms of Pauli matrices"
):
circuit()
@pytest.mark.parametrize(
("time", "hamiltonian", "steps", "gates"),
[
(
2,
qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)]),
2,
[
qml.PauliRot(2.0, "X", wires=[0]),
qml.PauliRot(2.0, "X", wires=[1]),
qml.PauliRot(2.0, "X", wires=[0]),
qml.PauliRot(2.0, "X", wires=[1]),
],
),
(
2,
qml.Hamiltonian([2, 0.5], [qml.PauliX("a"), qml.PauliZ("b") @ qml.PauliX("a")]),
2,
[
qml.PauliRot(4.0, "X", wires=["a"]),
qml.PauliRot(1.0, "ZX", wires=["b", "a"]),
qml.PauliRot(4.0, "X", wires=["a"]),
qml.PauliRot(1.0, "ZX", wires=["b", "a"]),
],
),
(
2,
qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.Identity(0) @ qml.Identity(1)]),
2,
[qml.PauliRot(2.0, "X", wires=[0]), qml.PauliRot(2.0, "X", wires=[0])],
),
(
2,
qml.Hamiltonian(
[2, 0.5, 0.5],
[
qml.PauliX("a"),
qml.PauliZ(-15) @ qml.PauliX("a"),
qml.Identity(0) @ qml.PauliY(-15),
],
),
1,
[
qml.PauliRot(8.0, "X", wires=["a"]),
qml.PauliRot(2.0, "ZX", wires=[-15, "a"]),
qml.PauliRot(2.0, "IY", wires=[0, -15]),
],
),
],
)
def test_evolution_operations(self, time, hamiltonian, steps, gates):
"""Tests that the sequence of gates implemented in the ApproxTimeEvolution template is correct"""
n_wires = 2
with qml._queuing.OperationRecorder() as rec:
ApproxTimeEvolution(hamiltonian, time, steps)
for i, gate in enumerate(rec.operations):
prep = [gate.parameters, gate.wires]
target = [gates[i].parameters, gates[i].wires]
assert prep == target
@pytest.mark.parametrize(
("time", "hamiltonian", "steps", "expectation"),
[
(np.pi, qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)]), 2, [1.0, 1.0]),
(
np.pi / 2,
qml.Hamiltonian([0.5, 1], [qml.PauliY(0), qml.Identity(0) @ qml.PauliX(1)]),
1,
[0.0, -1.0],
),
(
np.pi / 4,
qml.Hamiltonian(
[1, 1, 1], [qml.PauliX(0), qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliX(1)]
),
1,
[0.0, 0.0],
),
(
1,
qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)]),
2,
[-0.41614684, -0.41614684],
),
(
2,
qml.Hamiltonian(
[1, 1, 1, 1],
[qml.PauliX(0), qml.PauliY(0), qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliY(1)],
),
2,
[-0.87801124, 0.51725747],
),
],
)
def test_evolution_output(self, time, hamiltonian, steps, expectation):
"""Tests that the output from the ApproxTimeEvolution template is correct"""
n_wires = 2
dev = qml.device("default.qubit", wires=n_wires)
@qml.qnode(dev)
def circuit():
ApproxTimeEvolution(hamiltonian, time, steps)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]
assert np.allclose(circuit(), expectation)
class TestLayers:
"""Tests that the cost and mixer layers are being constructed properly"""
def test_mixer_layer_errors(self):
"""Tests that the mixer layer is throwing the correct errors"""
hamiltonian = [[1, 1], [1, 1]]
with pytest.raises(
ValueError,
match=r"hamiltonian must be of type pennylane.Hamiltonian"):
qaoa.mixer_layer(0.1, hamiltonian)
def test_cost_layer_errors(self):
"""Tests that the cost layer is throwing the correct errors"""
hamiltonian = [[1, 1], [1, 1]]
with pytest.raises(
ValueError,
match=r"hamiltonian must be of type pennylane.Hamiltonian"):
qaoa.cost_layer(0.1, hamiltonian)
hamiltonian = qml.Hamiltonian([1, 1], [qml.PauliZ(0), qml.PauliX(1)])
with pytest.raises(
ValueError,
match=
r"hamiltonian must be written only in terms of PauliZ and Identity gates"
):
qaoa.cost_layer(0.1, hamiltonian)
@pytest.mark.parametrize(
("mixer", "gates"), [[
qml.Hamiltonian([1, 1],
[qml.PauliX(0), qml.PauliX(1)]),
[qml.PauliRot(2, "X", wires=[0]),
qml.PauliRot(2, "X", wires=[1])]
],
[
qaoa.xy_mixer(Graph([(0, 1), (1, 2),
(2, 0)])),
[
qml.PauliRot(1, "XX", wires=[0, 1]),
qml.PauliRot(1, "YY", wires=[0, 1]),
qml.PauliRot(1, "XX", wires=[0, 2]),
qml.PauliRot(1, "YY", wires=[0, 2]),
qml.PauliRot(1, "XX", wires=[1, 2]),
qml.PauliRot(1, "YY", wires=[1, 2])
]
]])
def test_mixer_layer_output(self, mixer, gates):
"""Tests that the gates of the mixer layer are correct"""
alpha = 1
with qml._queuing.OperationRecorder() as rec:
qaoa.mixer_layer(alpha, mixer)
for i, j in zip(rec.operations, gates):
prep = [i.name, i.parameters, i.wires]
target = [j.name, j.parameters, j.wires]
assert prep == target
@pytest.mark.parametrize(
("cost", "gates"), [[
qml.Hamiltonian([1, 1],
[qml.PauliZ(0), qml.PauliZ(1)]),
[qml.PauliRot(2, "Z", wires=[0]),
qml.PauliRot(2, "Z", wires=[1])]
],
[
qaoa.maxcut(Graph([(0, 1), (1, 2),
(2, 0)]))[0],
[
qml.PauliRot(1, "ZZ", wires=[0, 1]),
qml.PauliRot(1, "ZZ", wires=[0, 2]),
qml.PauliRot(1, "ZZ", wires=[1, 2])
]
]])
def test_cost_layer_output(self, cost, gates):
"""Tests that the gates of the cost layer is correct"""
gamma = 1
with qml._queuing.OperationRecorder() as rec:
qaoa.cost_layer(gamma, cost)
for i, j in zip(rec.operations, gates):
prep = [i.name, i.parameters, i.wires]
target = [j.name, j.parameters, j.wires]
assert prep == target
def circuit(theta):
qml.PauliRot(theta, "XX", wires=[0, 1])
return qml.expval(qml.PauliZ(0))
"T": qml.T(wires=[0]),
"SX": qml.SX(wires=[0]),
"Toffoli": qml.Toffoli(wires=[0, 1, 2]),
"QFT": qml.templates.QFT(wires=[0, 1, 2]),
"IsingXX": qml.IsingXX(0, wires=[0, 1]),
"IsingYY": qml.IsingYY(0, wires=[0, 1]),
"IsingZZ": qml.IsingZZ(0, wires=[0, 1]),
"SingleExcitation": qml.SingleExcitation(0, wires=[0, 1]),
"SingleExcitationPlus": qml.SingleExcitationPlus(0, wires=[0, 1]),
"SingleExcitationMinus": qml.SingleExcitationMinus(0, wires=[0, 1]),
"DoubleExcitation": qml.DoubleExcitation(0, wires=[0, 1, 2, 3]),
"DoubleExcitationPlus": qml.DoubleExcitationPlus(0, wires=[0, 1, 2, 3]),
"DoubleExcitationMinus": qml.DoubleExcitationMinus(0, wires=[0, 1, 2, 3]),
"QubitCarry": qml.QubitCarry(wires=[0, 1, 2, 3]),
"QubitSum": qml.QubitSum(wires=[0, 1, 2]),
"PauliRot": qml.PauliRot(0, "XXYY", wires=[0, 1, 2, 3]),
"U1": qml.U1(0, wires=0),
"U2": qml.U2(0, 0, wires=0),
"U3": qml.U3(0, 0, 0, wires=0),
"SISWAP": qml.SISWAP(wires=[0, 1]),
}
all_ops = ops.keys()
# All qubit operations should be available to test in the device test suite
all_available_ops = qml.ops._qubit__ops__.copy() # pylint: disable=protected-access
all_available_ops.remove("CPhase") # CPhase is an alias of ControlledPhaseShift
all_available_ops.remove("SQISW") # SQISW is an alias of SISWAP
all_available_ops.add("QFT") # QFT was recently moved to being a template, but let's keep it here
if not set(all_ops) == all_available_ops:
class TestRepresentationResolver:
"""Test the RepresentationResolver class."""
@pytest.mark.parametrize(
"list,element,index,list_after",
[
([1, 2, 3], 2, 1, [1, 2, 3]),
([1, 2, 2, 3], 2, 1, [1, 2, 2, 3]),
([1, 2, 3], 4, 3, [1, 2, 3, 4]),
],
)
def test_index_of_array_or_append(self, list, element, index, list_after):
"""Test the method index_of_array_or_append."""
assert RepresentationResolver.index_of_array_or_append(element,
list) == index
assert list == list_after
@pytest.mark.parametrize(
"par,expected",
[
(3, "3"),
(5.236422, "5.24"),
],
)
def test_single_parameter_representation(self,
unicode_representation_resolver,
par, expected):
"""Test that single parameters are properly resolved."""
assert unicode_representation_resolver.single_parameter_representation(
par) == expected
@pytest.mark.parametrize(
"op,wire,target",
[
(qml.PauliX(wires=[1]), 1, "X"),
(qml.CNOT(wires=[0, 1]), 1, "X"),
(qml.CNOT(wires=[0, 1]), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]), 1, "X"),
(qml.Toffoli(wires=[0, 2, 1]), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]), 2, "C"),
(qml.CSWAP(wires=[0, 2, 1]), 1, "SWAP"),
(qml.CSWAP(wires=[0, 2, 1]), 2, "SWAP"),
(qml.CSWAP(wires=[0, 2, 1]), 0, "C"),
(qml.PauliY(wires=[1]), 1, "Y"),
(qml.PauliZ(wires=[1]), 1, "Z"),
(qml.CZ(wires=[0, 1]), 1, "Z"),
(qml.CZ(wires=[0, 1]), 0, "C"),
(qml.Identity(wires=[1]), 1, "I"),
(qml.Hadamard(wires=[1]), 1, "H"),
(qml.PauliRot(3.14, "XX", wires=[0, 1]), 1, "RX(3.14)"),
(qml.PauliRot(3.14, "YZ", wires=[0, 1]), 1, "RZ(3.14)"),
(qml.PauliRot(3.14, "IXYZI", wires=[0, 1, 2, 3, 4
]), 0, "RI(3.14)"),
(qml.PauliRot(3.14, "IXYZI", wires=[0, 1, 2, 3, 4
]), 1, "RX(3.14)"),
(qml.PauliRot(3.14, "IXYZI", wires=[0, 1, 2, 3, 4
]), 2, "RY(3.14)"),
(qml.PauliRot(3.14, "IXYZI", wires=[0, 1, 2, 3, 4
]), 3, "RZ(3.14)"),
(qml.PauliRot(3.14, "IXYZI", wires=[0, 1, 2, 3, 4
]), 4, "RI(3.14)"),
(qml.MultiRZ(3.14, wires=[0, 1]), 0, "RZ(3.14)"),
(qml.MultiRZ(3.14, wires=[0, 1]), 1, "RZ(3.14)"),
(qml.CRX(3.14, wires=[0, 1]), 1, "RX(3.14)"),
(qml.CRX(3.14, wires=[0, 1]), 0, "C"),
(qml.CRY(3.14, wires=[0, 1]), 1, "RY(3.14)"),
(qml.CRY(3.14, wires=[0, 1]), 0, "C"),
(qml.CRZ(3.14, wires=[0, 1]), 1, "RZ(3.14)"),
(qml.CRZ(3.14, wires=[0, 1]), 0, "C"),
(qml.CRot(3.14, 2.14, 1.14, wires=[0, 1
]), 1, "Rot(3.14, 2.14, 1.14)"),
(qml.CRot(3.14, 2.14, 1.14, wires=[0, 1]), 0, "C"),
(qml.PhaseShift(3.14, wires=[0]), 0, "Rϕ(3.14)"),
(qml.Beamsplitter(1, 2, wires=[0, 1]), 1, "BS(1, 2)"),
(qml.Beamsplitter(1, 2, wires=[0, 1]), 0, "BS(1, 2)"),
(qml.Squeezing(1, 2, wires=[1]), 1, "S(1, 2)"),
(qml.TwoModeSqueezing(1, 2, wires=[0, 1]), 1, "S(1, 2)"),
(qml.TwoModeSqueezing(1, 2, wires=[0, 1]), 0, "S(1, 2)"),
(qml.Displacement(1, 2, wires=[1]), 1, "D(1, 2)"),
(qml.NumberOperator(wires=[1]), 1, "n"),
(qml.Rotation(3.14, wires=[1]), 1, "R(3.14)"),
(qml.ControlledAddition(3.14, wires=[0, 1]), 1, "X(3.14)"),
(qml.ControlledAddition(3.14, wires=[0, 1]), 0, "C"),
(qml.ControlledPhase(3.14, wires=[0, 1]), 1, "Z(3.14)"),
(qml.ControlledPhase(3.14, wires=[0, 1]), 0, "C"),
(qml.ThermalState(3, wires=[1]), 1, "Thermal(3)"),
(
qml.GaussianState(np.array([[2, 0], [0, 2]]),
np.array([1, 2]),
wires=[1]),
1,
"Gaussian(M0,M1)",
),
(qml.QuadraticPhase(3.14, wires=[1]), 1, "P(3.14)"),
(qml.RX(3.14, wires=[1]), 1, "RX(3.14)"),
(qml.S(wires=[2]), 2, "S"),
(qml.T(wires=[2]), 2, "T"),
(qml.RX(3.14, wires=[1]), 1, "RX(3.14)"),
(qml.RY(3.14, wires=[1]), 1, "RY(3.14)"),
(qml.RZ(3.14, wires=[1]), 1, "RZ(3.14)"),
(qml.Rot(3.14, 2.14, 1.14, wires=[1]), 1, "Rot(3.14, 2.14, 1.14)"),
(qml.U1(3.14, wires=[1]), 1, "U1(3.14)"),
(qml.U2(3.14, 2.14, wires=[1]), 1, "U2(3.14, 2.14)"),
(qml.U3(3.14, 2.14, 1.14, wires=[1]), 1, "U3(3.14, 2.14, 1.14)"),
(qml.BasisState(np.array([0, 1, 0]), wires=[1, 2, 3]), 1, "|0⟩"),
(qml.BasisState(np.array([0, 1, 0]), wires=[1, 2, 3]), 2, "|1⟩"),
(qml.BasisState(np.array([0, 1, 0]), wires=[1, 2, 3]), 3, "|0⟩"),
(qml.QubitStateVector(np.array([0, 1, 0, 0]),
wires=[1, 2]), 1, "QubitStateVector(M0)"),
(qml.QubitStateVector(np.array([0, 1, 0, 0]),
wires=[1, 2]), 2, "QubitStateVector(M0)"),
(qml.QubitUnitary(np.eye(2), wires=[1]), 1, "U0"),
(qml.QubitUnitary(np.eye(4), wires=[1, 2]), 2, "U0"),
(qml.Kerr(3.14, wires=[1]), 1, "Kerr(3.14)"),
(qml.CrossKerr(3.14, wires=[1, 2]), 1, "CrossKerr(3.14)"),
(qml.CrossKerr(3.14, wires=[1, 2]), 2, "CrossKerr(3.14)"),
(qml.CubicPhase(3.14, wires=[1]), 1, "V(3.14)"),
(qml.InterferometerUnitary(
np.eye(4), wires=[1, 3]), 1, "InterferometerUnitary(M0)"),
(qml.InterferometerUnitary(
np.eye(4), wires=[1, 3]), 3, "InterferometerUnitary(M0)"),
(qml.CatState(3.14, 2.14, 1,
wires=[1]), 1, "CatState(3.14, 2.14, 1)"),
(qml.CoherentState(3.14, 2.14,
wires=[1]), 1, "CoherentState(3.14, 2.14)"),
(
qml.FockDensityMatrix(np.kron(np.eye(4), np.eye(4)),
wires=[1, 2]),
1,
"FockDensityMatrix(M0)",
),
(
qml.FockDensityMatrix(np.kron(np.eye(4), np.eye(4)),
wires=[1, 2]),
2,
"FockDensityMatrix(M0)",
),
(
qml.DisplacedSqueezedState(3.14, 2.14, 1.14, 0.14, wires=[1]),
1,
"DisplacedSqueezedState(3.14, 2.14, 1.14, 0.14)",
),
(qml.FockState(7, wires=[1]), 1, "|7⟩"),
(qml.FockStateVector(np.array([4, 5, 7]), wires=[1, 2, 3
]), 1, "|4⟩"),
(qml.FockStateVector(np.array([4, 5, 7]), wires=[1, 2, 3
]), 2, "|5⟩"),
(qml.FockStateVector(np.array([4, 5, 7]), wires=[1, 2, 3
]), 3, "|7⟩"),
(qml.SqueezedState(3.14, 2.14,
wires=[1]), 1, "SqueezedState(3.14, 2.14)"),
(qml.Hermitian(np.eye(4), wires=[1, 2]), 1, "H0"),
(qml.Hermitian(np.eye(4), wires=[1, 2]), 2, "H0"),
(qml.X(wires=[1]), 1, "x"),
(qml.P(wires=[1]), 1, "p"),
(qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3]), 1, "|4,5,7╳4,5,7|"),
(
qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1]),
2,
"1+2x₀-1.3x₁+6p₁",
),
(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1]),
1,
"1.2+1.1x₀+3.2p₀+1.2x₀²+2.3p₀²+3x₀p₀",
),
(
qml.PolyXP(
np.array([
[1.2, 2.3, 4.5, 0, 0],
[-1.2, 1.2, -1.5, 0, 0],
[-1.3, 4.5, 2.3, 0, 0],
[0, 2.6, 0, 0, 0],
[0, 0, 0, -4.7, -1.0],
]),
wires=[1],
),
1,
"1.2+1.1x₀+3.2p₀+1.2x₀²+2.3p₀²+3x₀p₀+2.6x₀x₁-p₁²-4.7x₁p₁",
),
(qml.QuadOperator(3.14, wires=[1]), 1, "cos(3.14)x+sin(3.14)p"),
(qml.PauliX(wires=[1]).inv(), 1, "X⁻¹"),
(qml.CNOT(wires=[0, 1]).inv(), 1, "X⁻¹"),
(qml.CNOT(wires=[0, 1]).inv(), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]).inv(), 1, "X⁻¹"),
(qml.Toffoli(wires=[0, 2, 1]).inv(), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]).inv(), 2, "C"),
(qml.measure.sample(wires=[0, 1]), 0,
"basis"), # not providing an observable in
(qml.measure.sample(wires=[0, 1]), 1,
"basis"), # sample gets displayed as raw
(two_wire_quantum_tape(), 0, "QuantumTape:T0"),
(two_wire_quantum_tape(), 1, "QuantumTape:T0"),
],
)
def test_operator_representation_unicode(self,
unicode_representation_resolver,
op, wire, target):
"""Test that an Operator instance is properly resolved."""
assert unicode_representation_resolver.operator_representation(
op, wire) == target
@pytest.mark.parametrize(
"op,wire,target",
[
(qml.PauliX(wires=[1]), 1, "X"),
(qml.CNOT(wires=[0, 1]), 1, "X"),
(qml.CNOT(wires=[0, 1]), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]), 1, "X"),
(qml.Toffoli(wires=[0, 2, 1]), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]), 2, "C"),
(qml.CSWAP(wires=[0, 2, 1]), 1, "SWAP"),
(qml.CSWAP(wires=[0, 2, 1]), 2, "SWAP"),
(qml.CSWAP(wires=[0, 2, 1]), 0, "C"),
(qml.PauliY(wires=[1]), 1, "Y"),
(qml.PauliZ(wires=[1]), 1, "Z"),
(qml.CZ(wires=[0, 1]), 1, "Z"),
(qml.CZ(wires=[0, 1]), 0, "C"),
(qml.Identity(wires=[1]), 1, "I"),
(qml.Hadamard(wires=[1]), 1, "H"),
(qml.CRX(3.14, wires=[0, 1]), 1, "RX(3.14)"),
(qml.CRX(3.14, wires=[0, 1]), 0, "C"),
(qml.CRY(3.14, wires=[0, 1]), 1, "RY(3.14)"),
(qml.CRY(3.14, wires=[0, 1]), 0, "C"),
(qml.CRZ(3.14, wires=[0, 1]), 1, "RZ(3.14)"),
(qml.CRZ(3.14, wires=[0, 1]), 0, "C"),
(qml.CRot(3.14, 2.14, 1.14, wires=[0, 1
]), 1, "Rot(3.14, 2.14, 1.14)"),
(qml.CRot(3.14, 2.14, 1.14, wires=[0, 1]), 0, "C"),
(qml.PhaseShift(3.14, wires=[0]), 0, "Rϕ(3.14)"),
(qml.Beamsplitter(1, 2, wires=[0, 1]), 1, "BS(1, 2)"),
(qml.Beamsplitter(1, 2, wires=[0, 1]), 0, "BS(1, 2)"),
(qml.Squeezing(1, 2, wires=[1]), 1, "S(1, 2)"),
(qml.TwoModeSqueezing(1, 2, wires=[0, 1]), 1, "S(1, 2)"),
(qml.TwoModeSqueezing(1, 2, wires=[0, 1]), 0, "S(1, 2)"),
(qml.Displacement(1, 2, wires=[1]), 1, "D(1, 2)"),
(qml.NumberOperator(wires=[1]), 1, "n"),
(qml.Rotation(3.14, wires=[1]), 1, "R(3.14)"),
(qml.ControlledAddition(3.14, wires=[0, 1]), 1, "X(3.14)"),
(qml.ControlledAddition(3.14, wires=[0, 1]), 0, "C"),
(qml.ControlledPhase(3.14, wires=[0, 1]), 1, "Z(3.14)"),
(qml.ControlledPhase(3.14, wires=[0, 1]), 0, "C"),
(qml.ThermalState(3, wires=[1]), 1, "Thermal(3)"),
(
qml.GaussianState(np.array([[2, 0], [0, 2]]),
np.array([1, 2]),
wires=[1]),
1,
"Gaussian(M0,M1)",
),
(qml.QuadraticPhase(3.14, wires=[1]), 1, "P(3.14)"),
(qml.RX(3.14, wires=[1]), 1, "RX(3.14)"),
(qml.S(wires=[2]), 2, "S"),
(qml.T(wires=[2]), 2, "T"),
(qml.RX(3.14, wires=[1]), 1, "RX(3.14)"),
(qml.RY(3.14, wires=[1]), 1, "RY(3.14)"),
(qml.RZ(3.14, wires=[1]), 1, "RZ(3.14)"),
(qml.Rot(3.14, 2.14, 1.14, wires=[1]), 1, "Rot(3.14, 2.14, 1.14)"),
(qml.U1(3.14, wires=[1]), 1, "U1(3.14)"),
(qml.U2(3.14, 2.14, wires=[1]), 1, "U2(3.14, 2.14)"),
(qml.U3(3.14, 2.14, 1.14, wires=[1]), 1, "U3(3.14, 2.14, 1.14)"),
(qml.BasisState(np.array([0, 1, 0]), wires=[1, 2, 3]), 1, "|0>"),
(qml.BasisState(np.array([0, 1, 0]), wires=[1, 2, 3]), 2, "|1>"),
(qml.BasisState(np.array([0, 1, 0]), wires=[1, 2, 3]), 3, "|0>"),
(qml.QubitStateVector(np.array([0, 1, 0, 0]),
wires=[1, 2]), 1, "QubitStateVector(M0)"),
(qml.QubitStateVector(np.array([0, 1, 0, 0]),
wires=[1, 2]), 2, "QubitStateVector(M0)"),
(qml.QubitUnitary(np.eye(2), wires=[1]), 1, "U0"),
(qml.QubitUnitary(np.eye(4), wires=[1, 2]), 2, "U0"),
(qml.Kerr(3.14, wires=[1]), 1, "Kerr(3.14)"),
(qml.CrossKerr(3.14, wires=[1, 2]), 1, "CrossKerr(3.14)"),
(qml.CrossKerr(3.14, wires=[1, 2]), 2, "CrossKerr(3.14)"),
(qml.CubicPhase(3.14, wires=[1]), 1, "V(3.14)"),
(qml.InterferometerUnitary(
np.eye(4), wires=[1, 3]), 1, "InterferometerUnitary(M0)"),
(qml.InterferometerUnitary(
np.eye(4), wires=[1, 3]), 3, "InterferometerUnitary(M0)"),
(qml.CatState(3.14, 2.14, 1,
wires=[1]), 1, "CatState(3.14, 2.14, 1)"),
(qml.CoherentState(3.14, 2.14,
wires=[1]), 1, "CoherentState(3.14, 2.14)"),
(
qml.FockDensityMatrix(np.kron(np.eye(4), np.eye(4)),
wires=[1, 2]),
1,
"FockDensityMatrix(M0)",
),
(
qml.FockDensityMatrix(np.kron(np.eye(4), np.eye(4)),
wires=[1, 2]),
2,
"FockDensityMatrix(M0)",
),
(
qml.DisplacedSqueezedState(3.14, 2.14, 1.14, 0.14, wires=[1]),
1,
"DisplacedSqueezedState(3.14, 2.14, 1.14, 0.14)",
),
(qml.FockState(7, wires=[1]), 1, "|7>"),
(qml.FockStateVector(np.array([4, 5, 7]), wires=[1, 2, 3
]), 1, "|4>"),
(qml.FockStateVector(np.array([4, 5, 7]), wires=[1, 2, 3
]), 2, "|5>"),
(qml.FockStateVector(np.array([4, 5, 7]), wires=[1, 2, 3
]), 3, "|7>"),
(qml.SqueezedState(3.14, 2.14,
wires=[1]), 1, "SqueezedState(3.14, 2.14)"),
(qml.Hermitian(np.eye(4), wires=[1, 2]), 1, "H0"),
(qml.Hermitian(np.eye(4), wires=[1, 2]), 2, "H0"),
(qml.X(wires=[1]), 1, "x"),
(qml.P(wires=[1]), 1, "p"),
(qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3]), 1, "|4,5,7X4,5,7|"),
(
qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1]),
2,
"1+2x_0-1.3x_1+6p_1",
),
(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1]),
1,
"1.2+1.1x_0+3.2p_0+1.2x_0^2+2.3p_0^2+3x_0p_0",
),
(
qml.PolyXP(
np.array([
[1.2, 2.3, 4.5, 0, 0],
[-1.2, 1.2, -1.5, 0, 0],
[-1.3, 4.5, 2.3, 0, 0],
[0, 2.6, 0, 0, 0],
[0, 0, 0, -4.7, 0],
]),
wires=[1],
),
1,
"1.2+1.1x_0+3.2p_0+1.2x_0^2+2.3p_0^2+3x_0p_0+2.6x_0x_1-4.7x_1p_1",
),
(qml.QuadOperator(3.14, wires=[1]), 1, "cos(3.14)x+sin(3.14)p"),
(qml.QuadOperator(3.14, wires=[1]), 1, "cos(3.14)x+sin(3.14)p"),
(qml.PauliX(wires=[1]).inv(), 1, "X^-1"),
(qml.CNOT(wires=[0, 1]).inv(), 1, "X^-1"),
(qml.CNOT(wires=[0, 1]).inv(), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]).inv(), 1, "X^-1"),
(qml.Toffoli(wires=[0, 2, 1]).inv(), 0, "C"),
(qml.Toffoli(wires=[0, 2, 1]).inv(), 2, "C"),
(qml.measure.sample(wires=[0, 1]), 0,
"basis"), # not providing an observable in
(qml.measure.sample(wires=[0, 1]), 1,
"basis"), # sample gets displayed as raw
(two_wire_quantum_tape(), 0, "QuantumTape:T0"),
(two_wire_quantum_tape(), 1, "QuantumTape:T0"),
],
)
def test_operator_representation_ascii(self, ascii_representation_resolver,
op, wire, target):
"""Test that an Operator instance is properly resolved."""
assert ascii_representation_resolver.operator_representation(
op, wire) == target
@pytest.mark.parametrize(
"obs,wire,target",
[
(qml.expval(qml.PauliX(wires=[1])), 1, "⟨X⟩"),
(qml.expval(qml.PauliY(wires=[1])), 1, "⟨Y⟩"),
(qml.expval(qml.PauliZ(wires=[1])), 1, "⟨Z⟩"),
(qml.expval(qml.Hadamard(wires=[1])), 1, "⟨H⟩"),
(qml.expval(qml.Hermitian(np.eye(4), wires=[1, 2])), 1, "⟨H0⟩"),
(qml.expval(qml.Hermitian(np.eye(4), wires=[1, 2])), 2, "⟨H0⟩"),
(qml.expval(qml.NumberOperator(wires=[1])), 1, "⟨n⟩"),
(qml.expval(qml.X(wires=[1])), 1, "⟨x⟩"),
(qml.expval(qml.P(wires=[1])), 1, "⟨p⟩"),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])),
1,
"⟨|4,5,7╳4,5,7|⟩",
),
(
qml.expval(qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1
])),
2,
"⟨1+2x₀-1.3x₁+6p₁⟩",
),
(
qml.expval(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1])),
1,
"⟨1.2+1.1x₀+3.2p₀+1.2x₀²+2.3p₀²+3x₀p₀⟩",
),
(qml.expval(qml.QuadOperator(
3.14, wires=[1])), 1, "⟨cos(3.14)x+sin(3.14)p⟩"),
(qml.var(qml.PauliX(wires=[1])), 1, "Var[X]"),
(qml.var(qml.PauliY(wires=[1])), 1, "Var[Y]"),
(qml.var(qml.PauliZ(wires=[1])), 1, "Var[Z]"),
(qml.var(qml.Hadamard(wires=[1])), 1, "Var[H]"),
(qml.var(qml.Hermitian(np.eye(4), wires=[1, 2])), 1, "Var[H0]"),
(qml.var(qml.Hermitian(np.eye(4), wires=[1, 2])), 2, "Var[H0]"),
(qml.var(qml.NumberOperator(wires=[1])), 1, "Var[n]"),
(qml.var(qml.X(wires=[1])), 1, "Var[x]"),
(qml.var(qml.P(wires=[1])), 1, "Var[p]"),
(
qml.var(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])),
1,
"Var[|4,5,7╳4,5,7|]",
),
(
qml.var(qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1])),
2,
"Var[1+2x₀-1.3x₁+6p₁]",
),
(
qml.var(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1])),
1,
"Var[1.2+1.1x₀+3.2p₀+1.2x₀²+2.3p₀²+3x₀p₀]",
),
(qml.var(qml.QuadOperator(
3.14, wires=[1])), 1, "Var[cos(3.14)x+sin(3.14)p]"),
(qml.sample(qml.PauliX(wires=[1])), 1, "Sample[X]"),
(qml.sample(qml.PauliY(wires=[1])), 1, "Sample[Y]"),
(qml.sample(qml.PauliZ(wires=[1])), 1, "Sample[Z]"),
(qml.sample(qml.Hadamard(wires=[1])), 1, "Sample[H]"),
(qml.sample(qml.Hermitian(np.eye(4), wires=[1, 2
])), 1, "Sample[H0]"),
(qml.sample(qml.Hermitian(np.eye(4), wires=[1, 2
])), 2, "Sample[H0]"),
(qml.sample(qml.NumberOperator(wires=[1])), 1, "Sample[n]"),
(qml.sample(qml.X(wires=[1])), 1, "Sample[x]"),
(qml.sample(qml.P(wires=[1])), 1, "Sample[p]"),
(
qml.sample(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])),
1,
"Sample[|4,5,7╳4,5,7|]",
),
(
qml.sample(qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1
])),
2,
"Sample[1+2x₀-1.3x₁+6p₁]",
),
(
qml.sample(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1])),
1,
"Sample[1.2+1.1x₀+3.2p₀+1.2x₀²+2.3p₀²+3x₀p₀]",
),
(qml.sample(qml.QuadOperator(
3.14, wires=[1])), 1, "Sample[cos(3.14)x+sin(3.14)p]"),
(
qml.expval(
qml.PauliX(wires=[1]) @ qml.PauliY(wires=[2])
@ qml.PauliZ(wires=[3])),
1,
"⟨X ⊗ Y ⊗ Z⟩",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
1,
"⟨|4,5,7╳4,5,7| ⊗ x⟩",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
2,
"⟨|4,5,7╳4,5,7| ⊗ x⟩",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
3,
"⟨|4,5,7╳4,5,7| ⊗ x⟩",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
4,
"⟨|4,5,7╳4,5,7| ⊗ x⟩",
),
(
qml.sample(
qml.Hermitian(np.eye(4), wires=[1, 2]) @ qml.Hermitian(
np.eye(4), wires=[0, 3])),
0,
"Sample[H0 ⊗ H0]",
),
(
qml.sample(
qml.Hermitian(np.eye(4), wires=[1, 2]) @ qml.Hermitian(
2 * np.eye(4), wires=[0, 3])),
0,
"Sample[H0 ⊗ H1]",
),
(qml.probs([0]), 0, "Probs"),
(state(), 0, "State"),
],
)
def test_output_representation_unicode(self,
unicode_representation_resolver,
obs, wire, target):
"""Test that an Observable instance with return type is properly resolved."""
assert unicode_representation_resolver.output_representation(
obs, wire) == target
def test_fallback_output_representation_unicode(
self, unicode_representation_resolver):
"""Test that an Observable instance with return type is properly resolved."""
obs = qml.PauliZ(0)
obs.return_type = "TestReturnType"
assert unicode_representation_resolver.output_representation(
obs, 0) == "TestReturnType[Z]"
@pytest.mark.parametrize(
"obs,wire,target",
[
(qml.expval(qml.PauliX(wires=[1])), 1, "<X>"),
(qml.expval(qml.PauliY(wires=[1])), 1, "<Y>"),
(qml.expval(qml.PauliZ(wires=[1])), 1, "<Z>"),
(qml.expval(qml.Hadamard(wires=[1])), 1, "<H>"),
(qml.expval(qml.Hermitian(np.eye(4), wires=[1, 2])), 1, "<H0>"),
(qml.expval(qml.Hermitian(np.eye(4), wires=[1, 2])), 2, "<H0>"),
(qml.expval(qml.NumberOperator(wires=[1])), 1, "<n>"),
(qml.expval(qml.X(wires=[1])), 1, "<x>"),
(qml.expval(qml.P(wires=[1])), 1, "<p>"),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])),
1,
"<|4,5,7X4,5,7|>",
),
(
qml.expval(qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1
])),
2,
"<1+2x_0-1.3x_1+6p_1>",
),
(
qml.expval(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1])),
1,
"<1.2+1.1x_0+3.2p_0+1.2x_0^2+2.3p_0^2+3x_0p_0>",
),
(qml.expval(qml.QuadOperator(
3.14, wires=[1])), 1, "<cos(3.14)x+sin(3.14)p>"),
(qml.var(qml.PauliX(wires=[1])), 1, "Var[X]"),
(qml.var(qml.PauliY(wires=[1])), 1, "Var[Y]"),
(qml.var(qml.PauliZ(wires=[1])), 1, "Var[Z]"),
(qml.var(qml.Hadamard(wires=[1])), 1, "Var[H]"),
(qml.var(qml.Hermitian(np.eye(4), wires=[1, 2])), 1, "Var[H0]"),
(qml.var(qml.Hermitian(np.eye(4), wires=[1, 2])), 2, "Var[H0]"),
(qml.var(qml.NumberOperator(wires=[1])), 1, "Var[n]"),
(qml.var(qml.X(wires=[1])), 1, "Var[x]"),
(qml.var(qml.P(wires=[1])), 1, "Var[p]"),
(
qml.var(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])),
1,
"Var[|4,5,7X4,5,7|]",
),
(
qml.var(qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1])),
2,
"Var[1+2x_0-1.3x_1+6p_1]",
),
(
qml.var(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1])),
1,
"Var[1.2+1.1x_0+3.2p_0+1.2x_0^2+2.3p_0^2+3x_0p_0]",
),
(qml.var(qml.QuadOperator(
3.14, wires=[1])), 1, "Var[cos(3.14)x+sin(3.14)p]"),
(qml.sample(qml.PauliX(wires=[1])), 1, "Sample[X]"),
(qml.sample(qml.PauliY(wires=[1])), 1, "Sample[Y]"),
(qml.sample(qml.PauliZ(wires=[1])), 1, "Sample[Z]"),
(qml.sample(qml.Hadamard(wires=[1])), 1, "Sample[H]"),
(qml.sample(qml.Hermitian(np.eye(4), wires=[1, 2
])), 1, "Sample[H0]"),
(qml.sample(qml.Hermitian(np.eye(4), wires=[1, 2
])), 2, "Sample[H0]"),
(qml.sample(qml.NumberOperator(wires=[1])), 1, "Sample[n]"),
(qml.sample(qml.X(wires=[1])), 1, "Sample[x]"),
(qml.sample(qml.P(wires=[1])), 1, "Sample[p]"),
(
qml.sample(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])),
1,
"Sample[|4,5,7X4,5,7|]",
),
(
qml.sample(qml.PolyXP(np.array([1, 2, 0, -1.3, 6]), wires=[1
])),
2,
"Sample[1+2x_0-1.3x_1+6p_1]",
),
(
qml.sample(
qml.PolyXP(np.array([[1.2, 2.3, 4.5], [-1.2, 1.2, -1.5],
[-1.3, 4.5, 2.3]]),
wires=[1])),
1,
"Sample[1.2+1.1x_0+3.2p_0+1.2x_0^2+2.3p_0^2+3x_0p_0]",
),
(qml.sample(qml.QuadOperator(
3.14, wires=[1])), 1, "Sample[cos(3.14)x+sin(3.14)p]"),
(
qml.expval(
qml.PauliX(wires=[1]) @ qml.PauliY(wires=[2])
@ qml.PauliZ(wires=[3])),
1,
"<X @ Y @ Z>",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
1,
"<|4,5,7X4,5,7| @ x>",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
2,
"<|4,5,7X4,5,7| @ x>",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
3,
"<|4,5,7X4,5,7| @ x>",
),
(
qml.expval(
qml.FockStateProjector(np.array([4, 5, 7]),
wires=[1, 2, 3])
@ qml.X(wires=[4])),
4,
"<|4,5,7X4,5,7| @ x>",
),
(
qml.sample(
qml.Hermitian(np.eye(4), wires=[1, 2]) @ qml.Hermitian(
np.eye(4), wires=[0, 3])),
0,
"Sample[H0 @ H0]",
),
(
qml.sample(
qml.Hermitian(np.eye(4), wires=[1, 2]) @ qml.Hermitian(
2 * np.eye(4), wires=[0, 3])),
0,
"Sample[H0 @ H1]",
),
(qml.probs([0]), 0, "Probs"),
(state(), 0, "State"),
],
)
def test_output_representation_ascii(self, ascii_representation_resolver,
obs, wire, target):
"""Test that an Observable instance with return type is properly resolved."""
assert ascii_representation_resolver.output_representation(
obs, wire) == target
def test_element_representation_none(self,
unicode_representation_resolver):
"""Test that element_representation properly handles None."""
assert unicode_representation_resolver.element_representation(None,
0) == ""
def test_element_representation_str(self, unicode_representation_resolver):
"""Test that element_representation properly handles strings."""
assert unicode_representation_resolver.element_representation(
"Test", 0) == "Test"
def test_element_representation_calls_output(
self, unicode_representation_resolver):
"""Test that element_representation calls output_representation for returned observables."""
unicode_representation_resolver.output_representation = Mock()
obs = qml.sample(qml.PauliX(3))
wire = 3
unicode_representation_resolver.element_representation(obs, wire)
assert unicode_representation_resolver.output_representation.call_args[
0] == (obs, wire)
def test_element_representation_calls_operator(
self, unicode_representation_resolver):
"""Test that element_representation calls operator_representation for all operators that are not returned."""
unicode_representation_resolver.operator_representation = Mock()
op = qml.PauliX(3)
wire = 3
unicode_representation_resolver.element_representation(op, wire)
assert unicode_representation_resolver.operator_representation.call_args[
0] == (op, wire)
def circuit_decomposed(time):
qml.PauliRot(time, "X", wires=[0])
qml.PauliRot(time, "X", wires=[1])
qml.PauliRot(time, "X", wires=[0])
qml.PauliRot(time, "X", wires=[1])
return qml.expval(qml.PauliZ(0))
def circuit_decomposed(weights):
for i in range(qml.math.shape(weights)[0]):
qml.PauliRot(weights[i], paulis_two_qubits[i], wires=[0, 1])
return qml.expval(qml.PauliZ(0))
def ApproxTimeEvolution(hamiltonian, time, n):
r"""Applies the Trotterized time-evolution operator for an arbitrary Hamiltonian, expressed in terms
of Pauli gates.
The general time-evolution operator for a time-independent Hamiltonian is given by
.. math:: U(t) \ = \ e^{-i H t},
for some Hamiltonian of the form:
.. math:: H \ = \ \displaystyle\sum_{j} H_j.
Implementing this unitary with a set of quantum gates is difficult, as the terms :math:`H_j` don't
necessarily commute with one another. However, we are able to exploit the Trotter-Suzuki decomposition formula,
.. math:: e^{A \ + \ B} \ = \ \lim_{n \to \infty} \Big[ e^{A/n} e^{B/n} \Big]^n,
to implement an approximation of the time-evolution operator as
.. math:: U \ \approx \ \displaystyle\prod_{k \ = \ 1}^{n} \displaystyle\prod_{j} e^{-i H_j t / n},
with the approximation becoming better for larger :math:`n`.
The circuit implementing this unitary is of the form:
.. figure:: ../../_static/templates/subroutines/approx_time_evolution.png
:align: center
:width: 60%
:target: javascript:void(0);
It is also important to note that
this decomposition is exact for any value of :math:`n` when each term of the Hamiltonian
commutes with every other term.
.. note::
This template uses the :class:`~.PauliRot` operation in order to implement
exponentiated terms of the input Hamiltonian. This operation only takes
terms that are explicitly written in terms of products of Pauli matrices (:class:`~.PauliX`,
:class:`~.PauliY`, :class:`~.PauliZ`, and :class:`~.Identity`).
Thus, each term in the Hamiltonian must be expressed this way upon input, or else an error will be raised.
Args:
hamiltonian (.Hamiltonian): The Hamiltonian defining the
time-evolution operator.
The Hamiltonian must be explicitly written
in terms of products of Pauli gates (:class:`~.PauliX`, :class:`~.PauliY`,
:class:`~.PauliZ`, and :class:`~.Identity`).
time (int or float): The time of evolution, namely the parameter :math:`t` in :math:`e^{- i H t}`.
n (int): The number of Trotter steps used when approximating the time-evolution operator.
Raises:
ValueError: if inputs do not have the correct format
.. UsageDetails::
The template is used inside a qnode:
.. code-block:: python
import pennylane as qml
from pennylane.templates import ApproxTimeEvolution
n_wires = 2
wires = range(n_wires)
dev = qml.device('default.qubit', wires=n_wires)
coeffs = [1, 1]
obs = [qml.PauliX(0), qml.PauliX(1)]
hamiltonian = qml.Hamiltonian(coeffs, obs)
@qml.qnode(dev)
def circuit(time):
ApproxTimeEvolution(hamiltonian, time, 1)
return [qml.expval(qml.PauliZ(wires=i)) for i in wires]
>>> circuit(1)
[-0.41614684 -0.41614684]
"""
_preprocess(hamiltonian)
pauli = {"Identity": "I", "PauliX": "X", "PauliY": "Y", "PauliZ": "Z"}
theta = []
pauli_words = []
wires = []
for i, term in enumerate(hamiltonian.ops):
word = ""
try:
if isinstance(term.name, str):
word = pauli[term.name]
if isinstance(term.name, list):
word = "".join(pauli[j] for j in term.name)
except KeyError as error:
raise ValueError(
"hamiltonian must be written in terms of Pauli matrices, got {}"
.format(error)) from error
# Skips terms composed solely of identities
if word.count("I") != len(word):
theta.append((2 * time * hamiltonian.coeffs[i]) / n)
pauli_words.append(word)
wires.append(term.wires)
for i in range(n):
for j, term in enumerate(pauli_words):
qml.PauliRot(theta[j], term, wires=wires[j])
class TestDecomposition:
"""Tests that the template defines the correct decomposition."""
@pytest.mark.parametrize(
("time", "hamiltonian", "steps", "expected_queue"),
[
(
2,
qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)]),
2,
[
qml.PauliRot(2.0, "X", wires=[0]),
qml.PauliRot(2.0, "X", wires=[1]),
qml.PauliRot(2.0, "X", wires=[0]),
qml.PauliRot(2.0, "X", wires=[1]),
],
),
(
2,
qml.Hamiltonian([2, 0.5], [qml.PauliX("a"), qml.PauliZ("b") @ qml.PauliX("a")]),
2,
[
qml.PauliRot(4.0, "X", wires=["a"]),
qml.PauliRot(1.0, "ZX", wires=["b", "a"]),
qml.PauliRot(4.0, "X", wires=["a"]),
qml.PauliRot(1.0, "ZX", wires=["b", "a"]),
],
),
(
2,
qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.Identity(0) @ qml.Identity(1)]),
2,
[qml.PauliRot(2.0, "X", wires=[0]), qml.PauliRot(2.0, "X", wires=[0])],
),
(
2,
qml.Hamiltonian(
[2, 0.5, 0.5],
[
qml.PauliX("a"),
qml.PauliZ(-15) @ qml.PauliX("a"),
qml.Identity(0) @ qml.PauliY(-15),
],
),
1,
[
qml.PauliRot(8.0, "X", wires=["a"]),
qml.PauliRot(2.0, "ZX", wires=[-15, "a"]),
qml.PauliRot(2.0, "IY", wires=[0, -15]),
],
),
],
)
def test_evolution_operations(self, time, hamiltonian, steps, expected_queue):
"""Tests that the sequence of gates implemented in the ApproxTimeEvolution template is correct"""
op = qml.ApproxTimeEvolution(hamiltonian, time, steps)
queue = op.expand().operations
for expected_gate, gate in zip(expected_queue, queue):
prep = [gate.parameters, gate.wires]
target = [expected_gate.parameters, expected_gate.wires]
assert prep == target
@pytest.mark.parametrize(
("time", "hamiltonian", "steps", "expectation"),
[
(np.pi, qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)]), 2, [1.0, 1.0]),
(
np.pi / 2,
qml.Hamiltonian([0.5, 1], [qml.PauliY(0), qml.Identity(0) @ qml.PauliX(1)]),
1,
[0.0, -1.0],
),
(
np.pi / 4,
qml.Hamiltonian(
[1, 1, 1], [qml.PauliX(0), qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliX(1)]
),
1,
[0.0, 0.0],
),
(
1,
qml.Hamiltonian([1, 1], [qml.PauliX(0), qml.PauliX(1)]),
2,
[-0.41614684, -0.41614684],
),
(
2,
qml.Hamiltonian(
[1, 1, 1, 1],
[qml.PauliX(0), qml.PauliY(0), qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliY(1)],
),
2,
[-0.87801124, 0.51725747],
),
],
)
def test_evolution_output(self, time, hamiltonian, steps, expectation):
"""Tests that the output from the ApproxTimeEvolution template is correct"""
n_wires = 2
dev = qml.device("default.qubit", wires=n_wires)
@qml.qnode(dev)
def circuit():
qml.ApproxTimeEvolution(hamiltonian, time, steps)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]
assert np.allclose(circuit(), expectation)
def test_custom_wire_labels(self, tol):
"""Test that template can deal with non-numeric, nonconsecutive wire labels."""
hamiltonian = qml.Hamiltonian([1, 1, 1], [qml.PauliX(0), qml.PauliX(1), qml.PauliX(2)])
hamiltonian2 = qml.Hamiltonian(
[1, 1, 1], [qml.PauliX("z"), qml.PauliX("a"), qml.PauliX("k")]
)
dev = qml.device("default.qubit", wires=3)
dev2 = qml.device("default.qubit", wires=["z", "a", "k"])
@qml.qnode(dev)
def circuit():
qml.ApproxTimeEvolution(hamiltonian, 0.5, 2)
return qml.expval(qml.Identity(0))
@qml.qnode(dev2)
def circuit2():
qml.ApproxTimeEvolution(hamiltonian2, 0.5, 2)
return qml.expval(qml.Identity("z"))
circuit()
circuit2()
assert np.allclose(dev.state, dev2.state, atol=tol, rtol=0)