def test_expected_tape(self):
"""Tests if QuantumPhaseEstimation populates the tape as expected for a fixed example"""
m = qml.RX(0.3, wires=0).matrix
op = qml.QuantumPhaseEstimation(m,
target_wires=[0],
estimation_wires=[1, 2])
tape = op.expand()
with qml.tape.QuantumTape() as tape2:
qml.Hadamard(1),
qml.ControlledQubitUnitary(m @ m, control_wires=[1], wires=[0]),
qml.Hadamard(2),
qml.ControlledQubitUnitary(m, control_wires=[2], wires=[0]),
qml.QFT(wires=[1, 2]).inv()
assert len(tape2.queue) == len(tape.queue)
assert all([
op1.name == op2.name for op1, op2 in zip(tape.queue, tape2.queue)
])
assert all([
op1.wires == op2.wires for op1, op2 in zip(tape.queue, tape2.queue)
])
assert np.allclose(tape.queue[1].matrix, tape2.queue[1].matrix)
assert np.allclose(tape.queue[3].matrix, tape2.queue[3].matrix)
def test_qubit_unitary():
"""Test ctrl on QubitUnitary and ControlledQubitUnitary"""
with QuantumTape() as tape:
ctrl(qml.QubitUnitary,
1)(np.array([[1.0, 1.0], [1.0, -1.0]]) / np.sqrt(2.0), wires=0)
tape = expand_tape(
tape, 3, stop_at=lambda op: not isinstance(op, ControlledOperation))
assert_equal_operations(tape.operations, [
qml.ControlledQubitUnitary(
np.array([[1.0, 1.0], [1.0, -1.0]]) / np.sqrt(2.0),
control_wires=1,
wires=0)
])
with QuantumTape() as tape:
ctrl(qml.ControlledQubitUnitary,
1)(np.array([[1.0, 1.0], [1.0, -1.0]]) / np.sqrt(2.0),
control_wires=2,
wires=0)
tape = expand_tape(
tape, 3, stop_at=lambda op: not isinstance(op, ControlledOperation))
assert_equal_operations(tape.operations, [
qml.ControlledQubitUnitary(
np.array([[1.0, 1.0], [1.0, -1.0]]) / np.sqrt(2.0),
control_wires=[1, 2],
wires=0)
])
def test_matrix(self):
"""Test if ControlledQubitUnitary returns the correct matrix for a control-control-X
(Toffoli) gate"""
mat = qml.ControlledQubitUnitary(X, control_wires=[0, 1],
wires=2).matrix
mat2 = qml.Toffoli(wires=[0, 1, 2]).matrix
assert np.allclose(mat, mat2)
def qfunc(a, b, c, angles):
qml.RX(a, wires=0)
qml.RX(b, wires=1)
qml.PauliZ(1)
qml.CNOT(wires=[0, 1]).inv()
qml.CRY(b, wires=[3, 1])
qml.RX(angles[0], wires=0)
qml.RX(4 * angles[1], wires=1)
qml.PhaseShift(17 / 9 * c, wires=2)
qml.RZ(b, wires=3)
qml.RX(angles[2], wires=2).inv()
qml.CRY(0.3589, wires=[3, 1]).inv()
qml.CSWAP(wires=[4, 2, 1]).inv()
qml.QubitUnitary(np.eye(2), wires=[2])
qml.ControlledQubitUnitary(np.eye(2), control_wires=[0, 1], wires=[2])
qml.MultiControlledX(control_wires=[0, 1, 2], wires=[3])
qml.Toffoli(wires=[0, 2, 1])
qml.CNOT(wires=[0, 2])
qml.PauliZ(wires=[1])
qml.PauliZ(wires=[1]).inv()
qml.CZ(wires=[0, 1])
qml.CZ(wires=[0, 2]).inv()
qml.CNOT(wires=[2, 1])
qml.CNOT(wires=[0, 2])
qml.SWAP(wires=[0, 2]).inv()
qml.CNOT(wires=[1, 3])
qml.RZ(b, wires=3)
qml.CSWAP(wires=[4, 0, 1])
return [
qml.expval(qml.PauliY(0)),
qml.var(qml.Hadamard(wires=1)),
qml.sample(qml.PauliX(2)),
qml.expval(qml.Hermitian(np.eye(4), wires=[3, 4])),
]
def test_apply(self, n_wires):
"""Test if the apply_controlled_Q performs the correct transformation by reconstructing the
unitary and comparing against the one provided in make_Q. Random unitaries are chosen for
a_mat and r_mat."""
n_all_wires = n_wires + 1
wires = range(n_wires)
target_wire = n_wires - 1
control_wire = n_wires
a_mat = unitary_group.rvs(2**(n_wires - 1), random_state=1967)
r_mat = unitary_group.rvs(2**n_wires, random_state=1967)
q_mat = make_Q(a_mat, r_mat)
def fn():
qml.QubitUnitary(a_mat, wires=wires[:-1])
qml.QubitUnitary(r_mat, wires=wires)
circ = apply_controlled_Q(fn,
wires=wires,
target_wire=target_wire,
control_wire=control_wire,
work_wires=None)
u = get_unitary(circ, n_all_wires)
circ = lambda: qml.ControlledQubitUnitary(
q_mat, wires=wires, control_wires=control_wire)
u_ideal = get_unitary(circ, n_all_wires)
assert np.allclose(u_ideal, u)
def f1():
qml.QubitUnitary(U1, wires=range(4))
qml.ControlledQubitUnitary(U,
control_wires=control_wires,
wires=target_wires)
qml.QubitUnitary(U2, wires=range(4))
return qml.state()
def circuit_mixed_polarity():
qml.templates.ArbitraryStatePreparation(control_state_weights, wires=control_wires)
qml.templates.ArbitraryStatePreparation(target_state_weights, wires=target_wires)
qml.ControlledQubitUnitary(
U, control_wires=control_wires, wires=target_wires, control_values=control_values
)
return qml.state()
def test_wrong_shape(self):
"""Test if ControlledQubitUnitary raises a ValueError if a unitary of shape inconsistent
with wires is provided"""
with pytest.raises(ValueError,
match=r"Input unitary must be of shape \(2, 2\)"):
qml.ControlledQubitUnitary(np.eye(4),
control_wires=[0, 1],
wires=2)
def test_invalid_mixed_polarity_controls(
self, control_wires, wires, control_values, expected_error_message
):
"""Test if ControlledQubitUnitary properly handles invalid mixed-polarity
control values."""
target_wires = Wires(wires)
with pytest.raises(ValueError, match=expected_error_message):
qml.ControlledQubitUnitary(
X, control_wires=control_wires, wires=target_wires, control_values=control_values
)
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 test_controlled_qubit_unitary_init(self):
"""Test for the init of ControlledQubitUnitary"""
control_wires = [3, 2]
target_wires = [1, 0]
U = qml.CRX._matrix(0.4)
op = qml.ControlledQubitUnitary(U, control_wires=control_wires, wires=target_wires)
target_data = [np.block([[np.eye(12), np.zeros((12, 4))], [np.zeros((4, 12)), U]])]
assert op.name == qml.ControlledQubitUnitary.__name__
assert np.allclose(target_data, op.data)
assert op._wires == Wires(control_wires) + Wires(target_wires)
def circuit_pauli_x():
qml.templates.ArbitraryStatePreparation(control_state_weights, wires=control_wires)
qml.templates.ArbitraryStatePreparation(target_state_weights, wires=target_wires)
for wire in x_locations:
qml.PauliX(wires=control_wires[wire])
qml.ControlledQubitUnitary(U, control_wires=control_wires, wires=wires)
for wire in x_locations:
qml.PauliX(wires=control_wires[wire])
return qml.state()
def expand(self):
unitary = self.parameters[0]
unitary_powers = [unitary]
for _ in range(len(self.estimation_wires) - 1):
new_power = unitary_powers[-1] @ unitary_powers[-1]
unitary_powers.append(new_power)
with qml.tape.QuantumTape() as tape:
for wire in self.estimation_wires:
qml.Hadamard(wire)
qml.ControlledQubitUnitary(unitary_powers.pop(),
control_wires=wire,
wires=self.target_wires)
qml.QFT(wires=self.estimation_wires).inv()
return tape
def parameterized_qubit_tape():
"""A parametrized qubit ciruit."""
a, b, c = 0.1, 0.2, 0.3
angles = np.array([0.4, 0.5, 0.6])
with qml.tape.QuantumTape() as tape:
qml.RX(a, wires=0)
qml.RX(b, wires=1)
qml.PauliZ(1)
qml.CNOT(wires=[0, 1]).inv()
qml.CRY(b, wires=[3, 1])
qml.RX(angles[0], wires=0)
qml.RX(4 * angles[1], wires=1)
qml.PhaseShift(17 / 9 * c, wires=2)
qml.RZ(b, wires=3)
qml.RX(angles[2], wires=2).inv()
qml.CRY(0.3589, wires=[3, 1]).inv()
qml.CSWAP(wires=[4, 2, 1]).inv()
qml.QubitUnitary(np.eye(2), wires=[2])
qml.ControlledQubitUnitary(np.eye(2), control_wires=[0, 1], wires=[2])
qml.MultiControlledX(control_wires=[0, 1, 2], wires=[3])
qml.Toffoli(wires=[0, 2, 1])
qml.CNOT(wires=[0, 2])
qml.PauliZ(wires=[1])
qml.PauliZ(wires=[1]).inv()
qml.CZ(wires=[0, 1])
qml.CZ(wires=[0, 2]).inv()
qml.CY(wires=[1, 2])
qml.CY(wires=[2, 0]).inv()
qml.CNOT(wires=[2, 1])
qml.CNOT(wires=[0, 2])
qml.SWAP(wires=[0, 2]).inv()
qml.CNOT(wires=[1, 3])
qml.RZ(b, wires=3)
qml.CSWAP(wires=[4, 0, 1])
qml.expval(qml.PauliY(0)),
qml.var(qml.Hadamard(wires=1)),
qml.sample(qml.PauliX(2)),
qml.expval(qml.Hermitian(np.eye(4), wires=[3, 4])),
return tape
def _get_gen_op(op, allow_nonunitary, aux_wire):
r"""Get the controlled-generator operation for a given operation.
Args:
op (pennylane.operation.Operation): Operation from which to extract the generator
allow_nonunitary (bool): Whether non-unitary gates are allowed in the circuit
aux_wire (int or pennylane.wires.Wires): Auxiliary wire on which to control the operation
Returns
qml.Operation: Controlled-generator operation of the generator of ``op``, controlled
on wire ``aux_wire``.
Raises
ValueError: If the generator of ``op`` is not known or it is non-unitary while
``allow_nonunitary=False``.
If ``allow_nonunitary=True``, a general :class:`~.pennylane.ControlledQubitUnitary` is returned,
otherwise only controlled Pauli operations are used. If the operation has a non-unitary
generator but ``allow_nonunitary=False``, the operation ``op`` should have been decomposed
before, leading to a ``ValueError``.
"""
gen, _ = op.generator
try:
if isinstance(gen, np.ndarray):
cgen = _OP_TO_CGEN[op.__class__]
else:
cgen = _GEN_TO_CGEN.get(gen, None)
if cgen is None:
cgen = _OP_TO_CGEN[op.__class__]
return cgen(wires=[aux_wire, *op.wires])
except KeyError as e:
if allow_nonunitary:
if (not isinstance(gen, np.ndarray)) and issubclass(
gen, qml.operation.Observable):
gen = gen.matrix
return qml.ControlledQubitUnitary(gen,
control_wires=aux_wire,
wires=op.wires)
raise ValueError(
f"Generator for operation {op} not known and non-unitary operations "
"deactivated via allow_nonunitary=False.") from e
def test_apply_controlled_v(n_wires):
"""Test if the _apply_controlled_v performs the correct transformation by reconstructing the
unitary and comparing against the one provided in _make_V."""
n_all_wires = n_wires + 1
wires = Wires(range(n_wires))
control_wire = Wires(n_wires)
circ = lambda: _apply_controlled_v(target_wire=Wires([n_wires - 1]),
control_wire=control_wire)
u = get_unitary(circ, n_all_wires)
# Note the sign flip in the following. The sign does not matter when performing the Q unitary
# because two Vs are used.
v_ideal = -_make_V(2**n_wires)
circ = lambda: qml.ControlledQubitUnitary(
v_ideal, wires=wires, control_wires=control_wire)
u_ideal = get_unitary(circ, n_all_wires)
assert np.allclose(u, u_ideal)
def expand_with_control(tape, control_wire):
"""Expand a tape to include a control wire on all queued operations.
Args:
tape (.QuantumTape): quantum tape to be controlled
control_wire (int): a single wire to use as the control wire
Returns:
.QuantumTape: A new QuantumTape with the controlled operations.
"""
with QuantumTape(do_queue=False) as new_tape:
for op in tape.operations:
if hasattr(op, "_controlled"):
# Execute the controlled version of the operation
# and add that the to the tape context.
# pylint: disable=protected-access
op._controlled(control_wire)
else:
# Attempt to decompose the operation and apply
# controls to each gate in the decomposition.
with new_tape.stop_recording():
try:
tmp_tape = op.expand()
except NotImplementedError:
# No decomposition is defined. Create a
# ControlledQubitUnitary gate using the operation
# matrix representation.
with QuantumTape() as tmp_tape:
qml.ControlledQubitUnitary(
op.matrix,
control_wires=control_wire,
wires=op.wires)
tmp_tape = expand_with_control(tmp_tape, control_wire)
requeue_ops_in_tape(tmp_tape)
return new_tape
"CRZ": qml.CRZ(0, wires=[0, 1]), "CRot": qml.CRot(0, 0, 0, wires=[0, 1]), "CSWAP": qml.CSWAP(wires=[0, 1, 2]), "CZ": qml.CZ(wires=[0, 1]), "CY": qml.CY(wires=[0, 1]), "DiagonalQubitUnitary": qml.DiagonalQubitUnitary(np.array([1, 1]), wires=[0]), "Hadamard": qml.Hadamard(wires=[0]), "MultiRZ": qml.MultiRZ(0, wires=[0]), "PauliX": qml.PauliX(wires=[0]), "PauliY": qml.PauliY(wires=[0]), "PauliZ": qml.PauliZ(wires=[0]), "PhaseShift": qml.PhaseShift(0, wires=[0]), "ControlledPhaseShift": qml.ControlledPhaseShift(0, wires=[0, 1]), "QubitStateVector": qml.QubitStateVector(np.array([1.0, 0.0]), wires=[0]), "QubitUnitary": qml.QubitUnitary(np.eye(2), wires=[0]), "ControlledQubitUnitary": qml.ControlledQubitUnitary(np.eye(2), control_wires=[1], wires=[0]), "MultiControlledX": qml.MultiControlledX(control_wires=[1, 2], wires=[0]), "RX": qml.RX(0, wires=[0]), "RY": qml.RY(0, wires=[0]), "RZ": qml.RZ(0, wires=[0]), "Rot": qml.Rot(0, 0, 0, wires=[0]), "S": qml.S(wires=[0]), "SWAP": qml.SWAP(wires=[0, 1]), "T": qml.T(wires=[0]), "SX": qml.SX(wires=[0]), "Toffoli": qml.Toffoli(wires=[0, 1, 2]), "QFT": qml.QFT(wires=[0, 1, 2]), "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]),
def test_shared_control(self):
"""Test if ControlledQubitUnitary raises an error if control wires are shared with wires"""
with pytest.raises(
ValueError,
match="The control wires must be different from the wires"):
qml.ControlledQubitUnitary(X, control_wires=[0, 2], wires=2)
def test_no_control(self):
"""Test if ControlledQubitUnitary raises an error if control wires are not specified"""
with pytest.raises(ValueError, match="Must specify control wires"):
qml.ControlledQubitUnitary(X, wires=2)
qml.PauliX(wires=control_wires[wire])
qml.ControlledQubitUnitary(U,
control_wires=control_wires,
wires=wires)
for wire in x_locations:
qml.PauliX(wires=control_wires[wire])
return qml.state()
mixed_polarity_state = circuit_mixed_polarity()
pauli_x_state = circuit_pauli_x()
assert np.allclose(mixed_polarity_state, pauli_x_state)
label_data = [
(qml.QubitUnitary(X, wires=0), "U"),
(qml.DiagonalQubitUnitary([1, 1], wires=1), "U"),
(qml.ControlledQubitUnitary(X, control_wires=0, wires=1), "U"),
]
@pytest.mark.parametrize("op, label", label_data)
def test_label(op, label):
assert op.label() == label
assert op.label(decimals=5) == label
op.inv()
assert op.label() == label + "⁻¹"
def QuantumPhaseEstimation(unitary, target_wires, estimation_wires):
r"""Performs the
`quantum phase estimation <https://en.wikipedia.org/wiki/Quantum_phase_estimation_algorithm>`__
circuit.
Given a unitary matrix :math:`U`, this template applies the circuit for quantum phase
estimation. The unitary is applied to the qubits specified by ``target_wires`` and :math:`n`
qubits are used for phase estimation as specified by ``estimation_wires``.
.. figure:: ../../_static/templates/subroutines/qpe.svg
:align: center
:width: 60%
:target: javascript:void(0);
This circuit can be used to perform the standard quantum phase estimation algorithm, consisting
of the following steps:
#. Prepare ``target_wires`` in a given state. If ``target_wires`` are prepared in an eigenstate
of :math:`U` that has corresponding eigenvalue :math:`e^{2 \pi i \theta}` with phase
:math:`\theta \in [0, 1)`, this algorithm will measure :math:`\theta`. Other input states can
be prepared more generally.
#. Apply the ``QuantumPhaseEstimation`` circuit.
#. Measure ``estimation_wires`` using :func:`~.probs`, giving a probability distribution over
measurement outcomes in the computational basis.
#. Find the index of the largest value in the probability distribution and divide that number by
:math:`2^{n}`. This number will be an estimate of :math:`\theta` with an error that decreases
exponentially with the number of qubits :math:`n`.
Note that if :math:`\theta \in (-1, 0]`, we can estimate the phase by again finding the index
:math:`i` found in step 4 and calculating :math:`\theta \approx \frac{1 - i}{2^{n}}`. The
usage details below give an example of this case.
Args:
unitary (array): the phase estimation unitary, specified as a matrix
target_wires (Union[Wires, Sequence[int], or int]): the target wires to apply the unitary
estimation_wires (Union[Wires, Sequence[int], or int]): the wires to be used for phase
estimation
Raises:
QuantumFunctionError: if the ``target_wires`` and ``estimation_wires`` share a common
element
.. UsageDetails::
Consider the matrix corresponding to a rotation from an :class:`~.RX` gate:
.. code-block:: python
import pennylane as qml
from pennylane.templates import QuantumPhaseEstimation
from pennylane import numpy as np
phase = 5
target_wires = [0]
unitary = qml.RX(phase, wires=0).matrix
The ``phase`` parameter can be estimated using ``QuantumPhaseEstimation``. An example is
shown below using a register of five phase-estimation qubits:
.. code-block:: python
n_estimation_wires = 5
estimation_wires = range(1, n_estimation_wires + 1)
dev = qml.device("default.qubit", wires=n_estimation_wires + 1)
@qml.qnode(dev)
def circuit():
# Start in the |+> eigenstate of the unitary
qml.Hadamard(wires=target_wires)
QuantumPhaseEstimation(
unitary,
target_wires=target_wires,
estimation_wires=estimation_wires,
)
return qml.probs(estimation_wires)
phase_estimated = np.argmax(circuit()) / 2 ** n_estimation_wires
# Need to rescale phase due to convention of RX gate
phase_estimated = 4 * np.pi * (1 - phase_estimated)
"""
target_wires = Wires(target_wires)
estimation_wires = Wires(estimation_wires)
if len(Wires.shared_wires([target_wires, estimation_wires])) != 0:
raise qml.QuantumFunctionError(
"The target wires and estimation wires must be different")
unitary_powers = [unitary]
for _ in range(len(estimation_wires) - 1):
new_power = unitary_powers[-1] @ unitary_powers[-1]
unitary_powers.append(new_power)
for wire in estimation_wires:
qml.Hadamard(wire)
qml.ControlledQubitUnitary(unitary_powers.pop(),
control_wires=wire,
wires=target_wires)
qml.QFT(wires=estimation_wires).inv()
def qfunc():
qml.PauliX(wires=2)
qml.ControlledQubitUnitary(np.array([[0, 1], [1, 0]]),
control_wires=0,
wires=2)
qml.PauliX(wires=2)