def adjoint_jacobian(self,
tape,
starting_state=None,
use_device_state=False):
"""Implements the adjoint method outlined in
`Jones and Gacon <https://arxiv.org/abs/2009.02823>`__ to differentiate an input tape.
After a forward pass, the circuit is reversed by iteratively applying inverse (adjoint)
gates to scan backwards through the circuit.
.. note::
The adjoint differentiation method has the following restrictions:
* As it requires knowledge of the statevector, only statevector simulator devices can be
used.
* Only expectation values are supported as measurements.
* Does not work for Hamiltonian observables.
Args:
tape (.QuantumTape): circuit that the function takes the gradient of
Keyword Args:
starting_state (tensor_like): post-forward pass state to start execution with. It should be
complex-valued. Takes precedence over ``use_device_state``.
use_device_state (bool): use current device state to initialize. A forward pass of the same
circuit should be the last thing the device has executed. If a ``starting_state`` is
provided, that takes precedence.
Returns:
array: the derivative of the tape with respect to trainable parameters.
Dimensions are ``(len(observables), len(trainable_params))``.
Raises:
QuantumFunctionError: if the input tape has measurements that are not expectation values
or contains a multi-parameter operation aside from :class:`~.Rot`
"""
# broadcasted inner product not summing over first dimension of b
sum_axes = tuple(range(1, self.num_wires + 1))
dot_product_real = lambda b, k: self._real(
qmlsum(self._conj(b) * k, axis=sum_axes))
for m in tape.measurements:
if m.return_type is not qml.operation.Expectation:
raise qml.QuantumFunctionError(
"Adjoint differentiation method does not support"
f" measurement {m.return_type.value}")
if m.obs.name == "Hamiltonian":
raise qml.QuantumFunctionError(
"Adjoint differentiation method does not support Hamiltonian observables."
)
if not hasattr(m.obs, "base_name"):
m.obs.base_name = None # This is needed for when the observable is a tensor product
if self.shots is not None:
warnings.warn(
"Requested adjoint differentiation to be computed with finite shots."
" The derivative is always exact when using the adjoint differentiation method.",
UserWarning,
)
# Initialization of state
if starting_state is not None:
ket = self._reshape(starting_state, [2] * self.num_wires)
else:
if not use_device_state:
self.reset()
self.execute(tape)
ket = self._pre_rotated_state
n_obs = len(tape.observables)
bras = np.empty([n_obs] + [2] * self.num_wires, dtype=np.complex128)
for kk in range(n_obs):
bras[kk, ...] = self._apply_operation(ket, tape.observables[kk])
expanded_ops = []
for op in reversed(tape.operations):
if op.num_params > 1:
if isinstance(op, qml.Rot) and not op.inverse:
ops = op.decompose()
expanded_ops.extend(reversed(ops))
else:
raise qml.QuantumFunctionError(
f"The {op.name} operation is not supported using "
'the "adjoint" differentiation method')
else:
if op.name not in ("QubitStateVector", "BasisState"):
expanded_ops.append(op)
jac = np.zeros((len(tape.observables), len(tape.trainable_params)))
param_number = len(tape._par_info) - 1 # pylint: disable=protected-access
trainable_param_number = len(tape.trainable_params) - 1
for op in expanded_ops:
if (op.grad_method is not None) and (param_number
in tape.trainable_params):
d_op_matrix = operation_derivative(op)
op.inv()
# Ideally use use op.adjoint() here
# then we don't have to re-invert the operation at the end
ket = self._apply_operation(ket, op)
if op.grad_method is not None:
if param_number in tape.trainable_params:
ket_temp = self._apply_unitary(ket, d_op_matrix, op.wires)
jac[:, trainable_param_number] = 2 * dot_product_real(
bras, ket_temp)
trainable_param_number -= 1
param_number -= 1
for kk in range(n_obs):
bras[kk, ...] = self._apply_operation(bras[kk, ...], op)
op.inv()
return jac
def adjoint_jacobian(self, tape):
"""Implements the adjoint method outlined in
`Jones and Gacon <https://arxiv.org/abs/2009.02823>`__ to differentiate an input tape.
After a forward pass, the circuit is reversed by iteratively applying inverse (adjoint)
gates to scan backwards through the circuit. This method is similar to the reversible
method, but has a lower time overhead and a similar memory overhead.
.. note::
The adjoint differentation method has the following restrictions:
* As it requires knowledge of the statevector, only statevector simulator devices can be
used.
* Only expectation values are supported as measurements.
Args:
tape (.QuantumTape): circuit that the function takes the gradient of
Returns:
array: the derivative of the tape with respect to trainable parameters.
Dimensions are ``(len(observables), len(trainable_params))``.
Raises:
QuantumFunctionError: if the input tape has measurements that are not expectation values
or contains a multi-parameter operation aside from :class:`~.Rot`
"""
for m in tape.measurements:
if m.return_type is not qml.operation.Expectation:
raise qml.QuantumFunctionError(
"Adjoint differentiation method does not support"
f" measurement {m.return_type.value}")
if not hasattr(m.obs, "base_name"):
m.obs.base_name = None # This is needed for when the observable is a tensor product
# Perform the forward pass.
# Consider using caching and calling lower-level functionality. We just need the device to
# be in the post-forward pass state.
# https://github.com/PennyLaneAI/pennylane/pull/1032/files#r563441040
self.reset()
self.execute(tape)
phi = self._reshape(self.state, [2] * self.num_wires)
lambdas = [self._apply_operation(phi, obs) for obs in tape.observables]
expanded_ops = []
for op in reversed(tape.operations):
if op.num_params > 1:
if isinstance(op, qml.Rot) and not op.inverse:
ops = op.decomposition(*op.parameters, wires=op.wires)
expanded_ops.extend(reversed(ops))
else:
raise QuantumFunctionError(
f"The {op.name} operation is not supported using "
'the "adjoint" differentiation method')
else:
if op.name not in ("QubitStateVector", "BasisState"):
expanded_ops.append(op)
jac = np.zeros((len(tape.observables), len(tape.trainable_params)))
dot_product_real = lambda a, b: self._real(qmlsum(self._conj(a) * b))
param_number = len(tape._par_info) - 1 # pylint: disable=protected-access
trainable_param_number = len(tape.trainable_params) - 1
for op in expanded_ops:
if (op.grad_method is not None) and (param_number
in tape.trainable_params):
d_op_matrix = operation_derivative(op)
op.inv()
phi = self._apply_operation(phi, op)
if op.grad_method is not None:
if param_number in tape.trainable_params:
mu = self._apply_unitary(phi, d_op_matrix, op.wires)
jac_column = np.array([
2 * dot_product_real(lambda_, mu)
for lambda_ in lambdas
])
jac[:, trainable_param_number] = jac_column
trainable_param_number -= 1
param_number -= 1
lambdas = [
self._apply_operation(lambda_, op) for lambda_ in lambdas
]
op.inv()
return jac