def _append_op(self, op):
"""Append a quantum operation into the circuit queue.
Args:
op (:class:`~.operation.Operation`): quantum operation to be added to the circuit
Raises:
ValueError: if `op` does not act on all wires
QuantumFunctionError: if state preparations and gates do not precede measured observables
"""
if op.num_wires == Wires.All:
if set(op.wires) != set(range(self.num_wires)):
raise QuantumFunctionError(
"Operator {} must act on all wires".format(op.name))
# Make sure only existing wires are used.
for w in _flatten(op.wires):
if w < 0 or w >= self.num_wires:
raise QuantumFunctionError(
"Operation {} applied to invalid wire {} "
"on device with {} wires.".format(op.name, w,
self.num_wires))
# observables go to their own, temporary queue
if isinstance(op, Observable):
if op.return_type is None:
self.queue.append(op)
else:
self.obs_queue.append(op)
else:
if self.obs_queue:
raise QuantumFunctionError(
"State preparations and gates must precede measured observables."
)
self.queue.append(op) # TODO rename self.queue to self.op_queue
def _default_args(self, kwargs):
"""Validate the quantum function arguments, apply defaults.
Here we apply default values for the auxiliary parameters of :attr:`QNode.func`.
Args:
kwargs (dict[str, Any]): auxiliary arguments (given using the keyword syntax)
Raises:
QuantumFunctionError: if the parameter to the quantum function was invalid
Returns:
dict[str, Any]: all auxiliary arguments (with defaults)
"""
forbidden_kinds = (
inspect.Parameter.POSITIONAL_ONLY,
inspect.Parameter.VAR_POSITIONAL,
inspect.Parameter.VAR_KEYWORD,
)
# check the validity of kwargs items
for name in kwargs:
s = self.func.sig.get(name)
if s is None:
if self.func.var_keyword:
continue # unknown parameter, but **kwargs will take it TODO should it?
raise QuantumFunctionError(
"Unknown quantum function parameter '{}'.".format(name))
if s.par.kind in forbidden_kinds or s.par.default == inspect.Parameter.empty:
raise QuantumFunctionError(
"Quantum function parameter '{}' cannot be given using the keyword syntax."
.format(name))
# apply defaults
for name, s in self.func.sig.items():
default = s.par.default
if default != inspect.Parameter.empty:
# meant to be given using keyword syntax
kwargs.setdefault(name, default)
return kwargs
def Interferometer(theta,
phi,
varphi,
wires,
mesh='rectangular',
beamsplitter='pennylane'):
r"""General linear interferometer, an array of beam splitters and phase shifters.
For :math:`M` wires, the general interferometer is specified by
providing :math:`M(M-1)/2` transmittivity angles :math:`\theta` and the same number of
phase angles :math:`\phi`, as well as either :math:`M-1` or :math:`M` additional rotation
parameters :math:`\varphi`.
For the parametrization of a universal interferometer
:math:`M-1` such rotation parameters are sufficient. If :math:`M` rotation
parameters are given, the interferometer is over-parametrized, but the resulting
circuit is more symmetric, which can be advantageous.
By specifying the keyword argument ``mesh``, the scheme used to implement the interferometer
may be adjusted:
* ``mesh='rectangular'`` (default): uses the scheme described in
:cite:`clements2016optimal`, resulting in a *rectangular* array of
:math:`M(M-1)/2` beamsplitters arranged in :math:`M` slices and ordered from left
to right and top to bottom in each slice. The first beamsplitter acts on
wires :math:`0` and :math:`1`:
.. figure:: ../../_static/clements.png
:align: center
:width: 30%
:target: javascript:void(0);
* ``mesh='triangular'``: uses the scheme described in :cite:`reck1994experimental`,
resulting in a *triangular* array of :math:`M(M-1)/2` beamsplitters arranged in
:math:`2M-3` slices and ordered from left to right and top to bottom. The
first and fourth beamsplitters act on wires :math:`M-1` and :math:`M`, the second
on :math:`M-2` and :math:`M-1`, and the third on :math:`M-3` and :math:`M-2`, and
so on.
.. figure:: ../../_static/reck.png
:align: center
:width: 30%
:target: javascript:void(0);
In both schemes, the network of :class:`~.Beamsplitter` operations is followed by
:math:`M` (or :math:`M-1`) local :class:`Rotation` Operations. In the latter case, the
rotation on the last wire is left out.
The rectangular decomposition is generally advantageous, as it has a lower
circuit depth (:math:`M` vs :math:`2M-3`) and optical depth than the triangular
decomposition, resulting in reduced optical loss.
This is an example of a 4-mode interferometer with beamsplitters :math:`B` and rotations :math:`R`,
using ``mesh='rectangular'``:
.. figure:: ../../_static/layer_interferometer.png
:align: center
:width: 60%
:target: javascript:void(0);
.. note::
The decomposition as formulated in :cite:`clements2016optimal` uses a different
convention for a beamsplitter :math:`T(\theta, \phi)` than PennyLane, namely:
.. math:: T(\theta, \phi) = BS(\theta, 0) R(\phi)
For the universality of the decomposition, the used convention is irrelevant, but
for a given set of angles the resulting interferometers will be different.
If an interferometer consistent with the convention from :cite:`clements2016optimal`
is needed, the optional keyword argument ``beamsplitter='clements'`` can be specified. This
will result in each :class:`~.Beamsplitter` being preceded by a :class:`Rotation` and
thus increase the number of elementary operations in the circuit.
Args:
theta (array): length :math:`M(M-1)/2` array of transmittivity angles :math:`\theta`
phi (array): length :math:`M(M-1)/2` array of phase angles :math:`\phi`
varphi (array): length :math:`M` or :math:`M-1` array of rotation angles :math:`\varphi`
wires (Sequence[int]): wires the interferometer should act on
Keyword Args:
mesh (string): the type of mesh to use
beamsplitter (str): if ``clements``, the beamsplitter convention from
Clements et al. 2016 (https://dx.doi.org/10.1364/OPTICA.3.001460) is used; if ``pennylane``, the
beamsplitter is implemented via PennyLane's ``Beamsplitter`` operation.
"""
if isinstance(beamsplitter, Variable):
raise QuantumFunctionError(
"The beamsplitter parameter influences the "
"circuit architecture and can not be passed as a QNode parameter.")
if isinstance(mesh, Variable):
raise QuantumFunctionError(
"The mesh parameter influences the circuit architecture "
"and can not be passed as a QNode parameter.")
if not isinstance(wires, Sequence):
w = [wires]
else:
w = wires
M = len(w)
if M == 1:
# the interferometer is a single rotation
Rotation(varphi[0], wires=w[0])
return
n = 0 # keep track of free parameters
if mesh == 'rectangular':
# Apply the Clements beamsplitter array
# The array depth is N
for l in range(M):
for k, (w1, w2) in enumerate(zip(w[:-1], w[1:])):
#skip even or odd pairs depending on layer
if (l + k) % 2 != 1:
if beamsplitter == 'clements':
Rotation(phi[n], wires=[w1])
Beamsplitter(theta[n], 0, wires=[w1, w2])
else:
Beamsplitter(theta[n], phi[n], wires=[w1, w2])
n += 1
elif mesh == 'triangular':
# apply the Reck beamsplitter array
# The array depth is 2*N-3
for l in range(2 * M - 3):
for k in range(abs(l + 1 - (M - 1)), M - 1, 2):
if beamsplitter == 'clements':
Rotation(phi[n], wires=[w[k]])
Beamsplitter(theta[n], 0, wires=[w[k], w[k + 1]])
else:
Beamsplitter(theta[n], phi[n], wires=[w[k], w[k + 1]])
n += 1
# apply the final local phase shifts to all modes
for i, p in enumerate(varphi):
Rotation(p, wires=[w[i]])
def _construct_metric_tensor(self, *, diag_approx=False):
"""Construct metric tensor subcircuits for qubit circuits.
Constructs a set of quantum circuits for computing a block-diagonal approximation of the
Fubini-Study metric tensor on the parameter space of the variational circuit represented
by the QNode, using the Quantum Geometric Tensor.
If the parameter appears in a gate :math:`G`, the subcircuit contains
all gates which precede :math:`G`, and :math:`G` is replaced by the variance
value of its generator.
Args:
diag_approx (bool): iff True, use the diagonal approximation
Raises:
QuantumFunctionError: if a metric tensor cannot be generated because no generator
was defined
"""
# pylint: disable=too-many-statements, too-many-branches
self._metric_tensor_subcircuits = {}
for queue, curr_ops, param_idx, _ in self.circuit.iterate_layers():
obs = []
scale = []
Ki_matrices = []
KiKj_matrices = []
Ki_ev = []
KiKj_ev = []
V = None
# for each operation in the layer, get the generator and convert it to a variance
for n, op in enumerate(curr_ops):
gen, s = op.generator
w = op.wires
if gen is None:
raise QuantumFunctionError(
"Can't generate metric tensor, operation {}"
"has no defined generator".format(op))
# get the observable corresponding to the generator of the current operation
if isinstance(gen, np.ndarray):
# generator is a Hermitian matrix
variance = var(qml.Hermitian(gen, w, do_queue=False))
if not diag_approx:
Ki_matrices.append((n, expand(gen, w, self.num_wires)))
elif issubclass(gen, Observable):
# generator is an existing PennyLane operation
variance = var(gen(w, do_queue=False))
if not diag_approx:
if issubclass(gen, qml.PauliX):
mat = np.array([[0, 1], [1, 0]])
elif issubclass(gen, qml.PauliY):
mat = np.array([[0, -1j], [1j, 0]])
elif issubclass(gen, qml.PauliZ):
mat = np.array([[1, 0], [0, -1]])
Ki_matrices.append((n, expand(mat, w, self.num_wires)))
else:
raise QuantumFunctionError(
"Can't generate metric tensor, generator {}"
"has no corresponding observable".format(gen))
obs.append(variance)
scale.append(s)
if not diag_approx:
# In order to compute the block diagonal portion of the metric tensor,
# we need to compute 'second order' <psi|K_i K_j|psi> terms.
for i, j in itertools.product(range(len(Ki_matrices)),
repeat=2):
# compute the matrices representing all K_i K_j terms
obs1 = Ki_matrices[i]
obs2 = Ki_matrices[j]
KiKj_matrices.append(
((obs1[0], obs2[0]), obs1[1] @ obs2[1]))
V = np.identity(2**self.num_wires, dtype=np.complex128)
# generate the unitary operation to rotate to
# the shared eigenbasis of all observables
for _, term in Ki_matrices:
_, S = linalg.eigh(V.conj().T @ term @ V)
V = np.round(V @ S, 15)
V = V.conj().T
# calculate the eigenvalues for
# each observable in the shared eigenbasis
for idx, term in Ki_matrices:
eigs = np.diag(V @ term @ V.conj().T).real
Ki_ev.append((idx, eigs))
for idx, term in KiKj_matrices:
eigs = np.diag(V @ term @ V.conj().T).real
KiKj_ev.append((idx, eigs))
self._metric_tensor_subcircuits[param_idx] = {
"queue": queue,
"observable": obs,
"Ki_expectations": Ki_ev,
"KiKj_expectations": KiKj_ev,
"eigenbasis_matrix": V,
"result": None,
"scale": scale,
}
def _check_circuit(self, res):
"""Check that the generated Operator queue corresponds to a valid quantum circuit.
.. note:: The validity of individual Operators is checked already in :meth:`_append_op`.
Args:
res (Sequence[Observable], Observable): output returned by the quantum function
Raises:
QuantumFunctionError: an error was discovered in the circuit
"""
# pylint: disable=too-many-branches
# check the return value
if isinstance(res, Observable):
if res.return_type is ObservableReturnTypes.Sample:
# Squeezing ensures that there is only one array of values returned
# when only a single-mode sample is requested
self.output_conversion = np.squeeze
else:
self.output_conversion = float
self.output_dim = 1
res = (res, )
elif isinstance(res, Sequence) and res and all(
isinstance(x, Observable) for x in res):
# for multiple observables values, any valid Python sequence of observables
# (i.e., lists, tuples, etc) are supported in the QNode return statement.
# Device already returns the correct numpy array, so no further conversion is required
self.output_conversion = np.asarray
self.output_dim = len(res)
res = tuple(res)
else:
raise QuantumFunctionError(
"A quantum function must return either a single measured observable "
"or a nonempty sequence of measured observables.")
# check that all returned observables have a return_type specified
for x in res:
if x.return_type is None:
raise QuantumFunctionError(
"Observable '{}' does not have the measurement type specified."
.format(x))
# check that all ev's are returned, in the correct order
if res != tuple(self.obs_queue):
raise QuantumFunctionError(
"All measured observables must be returned in the order they are measured."
)
# check that no wires are measured more than once
m_wires = list(w for ob in res for w in _flatten(ob.wires))
if len(m_wires) != len(set(m_wires)):
raise QuantumFunctionError(
"Each wire in the quantum circuit can only be measured once.")
# True if op is a CV, False if it is a discrete variable (Identity could be either)
are_cvs = [
isinstance(op, CV) for op in self.queue + list(res)
if not isinstance(op, qml.Identity)
]
if not all(are_cvs) and any(are_cvs):
raise QuantumFunctionError(
"Continuous and discrete operations are not allowed in the same quantum circuit."
)
if any(are_cvs) and self.type == "qubit":
raise QuantumFunctionError(
"Device {} is a qubit device; CV operations are not allowed.".
format(self.device.short_name))
if not all(are_cvs) and self.type == "cv":
raise QuantumFunctionError(
"Device {} is a CV device; qubit operations are not allowed.".
format(self.device.short_name))
queue = self.queue
if self.device.operations:
# replace operations in the queue with any decompositions if required
queue = decompose_queue(self.queue, self.device)
self.ops = queue + list(res)
del self.queue
del self.obs_queue
def _construct(self, args, kwargs):
"""Construct the quantum circuit graph by calling the quantum function.
For immutable nodes this method is called the first time :meth:`QNode.evaluate`
or :meth:`QNode.jacobian` is called, and for mutable nodes *each time*
they are called. It executes the quantum function,
stores the resulting sequence of :class:`.Operator` instances,
converts it into a circuit graph, and creates the Variable mapping.
.. note::
The Variables are only required for analytic differentiation,
for evaluation we could simply reconstruct the circuit each time.
Args:
args (tuple[Any]): Positional arguments passed to the quantum function.
During the construction we are not concerned with the numerical values, but with
the nesting structure.
Each positional argument is replaced with a :class:`~.variable.Variable` instance.
kwargs (dict[str, Any]): Auxiliary arguments passed to the quantum function.
Raises:
QuantumFunctionError: if the :class:`pennylane.QNode`'s _current_context is attempted to be modified
inside of this method, the quantum function returns incorrect values or if
both continuous and discrete operations are specified in the same quantum circuit
"""
# pylint: disable=protected-access # remove when QNode_old is gone
# pylint: disable=attribute-defined-outside-init, too-many-branches
self.args_model = (
args #: nested Sequence[Number]: nested shape of the arguments for later unflattening
)
# flatten the args, replace each argument with a Variable instance carrying a unique index
arg_vars = [Variable(idx) for idx, _ in enumerate(_flatten(args))]
self.num_variables = len(arg_vars)
# arrange the newly created Variables in the nested structure of args
arg_vars = unflatten(arg_vars, args)
# temporary queues for operations and observables
self.queue = [] #: list[Operation]: applied operations
self.obs_queue = [] #: list[Observable]: applied observables
# set up the context for Operator entry
if QNode_old._current_context is None:
QNode_old._current_context = self
else:
raise QuantumFunctionError(
"QNode._current_context must not be modified outside this method."
)
try:
# generate the program queue by executing the quantum circuit function
if self.mutable:
# it's ok to directly pass auxiliary arguments since the circuit is re-constructed each time
# (positional args must be replaced because parameter-shift differentiation requires Variables)
res = self.func(*arg_vars, **kwargs)
else:
# must convert auxiliary arguments to named Variables so they can be updated without re-constructing the circuit
kwarg_vars = {}
for key, val in kwargs.items():
temp = [
Variable(idx, name=key)
for idx, _ in enumerate(_flatten(val))
]
kwarg_vars[key] = unflatten(temp, val)
res = self.func(*arg_vars, **kwarg_vars)
finally:
QNode_old._current_context = None
# check the validity of the circuit
self._check_circuit(res)
# map each free variable to the operators which depend on it
self.variable_deps = {}
for k, op in enumerate(self.ops):
for j, p in enumerate(_flatten(op.params)):
if isinstance(p, Variable):
if p.name is None: # ignore auxiliary arguments
self.variable_deps.setdefault(p.idx, []).append(
ParameterDependency(op, j))
# generate the DAG
self.circuit = CircuitGraph(self.ops, self.variable_deps)
# check for operations that cannot affect the output
if self.properties.get("vis_check", False):
visible = self.circuit.ancestors(self.circuit.observables)
invisible = set(self.circuit.operations) - visible
if invisible:
raise QuantumFunctionError(
"The operations {} cannot affect the output of the circuit."
.format(invisible))