def test_circuit_modified(self):
"""tests that circuits don't get modified on QI execute with error mitigation
as per issue #7449
"""
algorithm_globals.random_seed = 1679
np.random.seed(algorithm_globals.random_seed)
circuit = QuantumCircuit(1)
circuit.x(0)
circuit.measure_all()
qi = QuantumInstance(
Aer.get_backend("aer_simulator"),
seed_simulator=algorithm_globals.random_seed,
seed_transpiler=algorithm_globals.random_seed,
shots=1024,
measurement_error_mitigation_cls=CompleteMeasFitter,
)
# The error happens on transpiled circuits since "execute" was changing the input array
# Non transpiled circuits didn't have a problem because a new transpiled array was created
# internally.
circuits_ref = qi.transpile(circuit) # always returns a new array
circuits_input = circuits_ref.copy()
_ = qi.execute(circuits_input, had_transpiled=True)
self.assertEqual(circuits_ref,
circuits_input,
msg="Transpiled circuit array modified.")
class QuantumKernel:
r"""Quantum Kernel.
The general task of machine learning is to find and study patterns in data. For many
algorithms, the datapoints are better understood in a higher dimensional feature space,
through the use of a kernel function:
.. math::
K(x, y) = \langle f(x), f(y)\rangle.
Here K is the kernel function, x, y are n dimensional inputs. f is a map from n-dimension
to m-dimension space. :math:`\langle x, y \rangle` denotes the dot product.
Usually m is much larger than n.
The quantum kernel algorithm calculates a kernel matrix, given datapoints x and y and feature
map f, all of n dimension. This kernel matrix can then be used in classical machine learning
algorithms such as support vector classification, spectral clustering or ridge regression.
"""
@deprecate_arguments("0.5.0", {"user_parameters": "training_parameters"})
def __init__(
self,
feature_map: Optional[QuantumCircuit] = None,
enforce_psd: bool = True,
batch_size: int = 900,
quantum_instance: Optional[Union[QuantumInstance, Backend]] = None,
training_parameters: Optional[Union[ParameterVector,
Sequence[Parameter]]] = None,
) -> None:
"""
Args:
feature_map: Parameterized circuit to be used as the feature map. If None is given,
the `ZZFeatureMap` is used with two qubits.
enforce_psd: Project to closest positive semidefinite matrix if x = y.
Only enforced when not using the state vector simulator. Default True.
batch_size: Number of circuits to batch together for computation. Default 900.
quantum_instance: Quantum Instance or Backend
training_parameters: Iterable containing ``Parameter`` objects which correspond to
quantum gates on the feature map circuit which may be tuned. If users intend to
tune feature map parameters to find optimal values, this field should be set.
"""
# Class fields
self._feature_map = None
self._unbound_feature_map = None
self._training_parameters = None
self._training_parameter_binds = None
self._enforce_psd = enforce_psd
self._batch_size = batch_size
self._quantum_instance = quantum_instance
# Setters
self.feature_map = feature_map if feature_map is not None else ZZFeatureMap(
2)
if training_parameters is not None:
self.training_parameters = training_parameters
@property
def feature_map(self) -> QuantumCircuit:
"""Return feature map"""
return self._feature_map
@feature_map.setter
def feature_map(self, feature_map: QuantumCircuit) -> None:
"""
Set feature map.
The ``unbound_feature_map`` field will be automatically updated when this field is set,
and ``training_parameters`` and ``training_parameter_binds`` fields will be reset to ``None``.
"""
self._feature_map = feature_map
self._unbound_feature_map = copy.deepcopy(self._feature_map)
self._training_parameters = None
self._training_parameter_binds = None
@property
def unbound_feature_map(self) -> QuantumCircuit:
"""Return unbound feature map"""
return copy.deepcopy(self._unbound_feature_map)
@property
def quantum_instance(self) -> QuantumInstance:
"""Return quantum instance"""
return self._quantum_instance
@quantum_instance.setter
def quantum_instance(
self, quantum_instance: Union[Backend, QuantumInstance]) -> None:
"""Set quantum instance"""
if isinstance(quantum_instance, Backend):
self._quantum_instance = QuantumInstance(quantum_instance)
else:
self._quantum_instance = quantum_instance
@property
def training_parameters(
self) -> Optional[Union[ParameterVector, Sequence[Parameter]]]:
"""Return the vector of training parameters."""
return copy.copy(self._training_parameters)
@training_parameters.setter
def training_parameters(
self, training_params: Union[ParameterVector,
Sequence[Parameter]]) -> None:
"""Set the training parameters"""
self._training_parameter_binds = {
training_params[i]: training_params[i]
for i, _ in enumerate(training_params)
}
self._training_parameters = copy.deepcopy(training_params)
def assign_training_parameters(
self, values: Union[Mapping[Parameter, ParameterValueType],
Sequence[ParameterValueType]]
) -> None:
"""
Assign training parameters in the ``QuantumKernel`` feature map.
Args:
values (dict or iterable): Either a dictionary or iterable specifying the new
parameter values. If a dict, it specifies the mapping from ``current_parameter`` to
``new_parameter``, where ``new_parameter`` can be a parameter expression or a
numeric value. If an iterable, the elements are assigned to the existing parameters
in the order of ``QuantumKernel.training_parameters``.
Raises:
ValueError: Incompatible number of training parameters and values
"""
if self._training_parameters is None:
raise ValueError(f"""
The number of parameter values ({len(values)}) does not
match the number of training parameters tracked by the QuantumKernel
(None).
""")
# Get the input parameters. These should remain unaffected by assigning of training parameters.
input_params = list(
set(self._unbound_feature_map.parameters) -
set(self._training_parameters))
# If iterable of values is passed, the length must match length of training_parameters field
if isinstance(values, (Sequence, np.ndarray)):
if len(values) != len(self._training_parameters):
raise ValueError(f"""
The number of parameter values ({len(values)}) does not
match the number of training parameters tracked by the QuantumKernel
({len(self._training_parameters)}).
""")
values = {
p: values[i]
for i, p in enumerate(self._training_parameters)
}
else:
if not isinstance(values, dict):
raise ValueError(f"""
'values' must be of type Dict or Sequence.
Type {type(values)} is not supported.
""")
# All input keys must exist in the circuit
# This check actually catches some well defined assignments;
# however; we throw an error to be consistent with the behavior
# of QuantumCircuit's parameter binding.
unknown_parameters = list(
set(values.keys()) - set(self._training_parameters))
if len(unknown_parameters) > 0:
raise ValueError(
f"Cannot bind parameters ({unknown_parameters}) not tracked by the quantum kernel."
)
# Because QuantumKernel supports parameter rebinding, entries of the `values` dictionary must
# be handled differently depending on whether they represent numerical assignments or parameter
# reassignments. However, re-ordering the values dictionary inherently changes the expected
# behavior of parameter binding, as entries in the values dict do not commute with one another
# in general. To resolve this issue, we handle each entry of the values dict one at a time.
for param, bind in values.items():
if isinstance(bind, ParameterExpression):
self._unbound_feature_map.assign_parameters({param: bind},
inplace=True)
# Training params are all non-input params in the unbound feature map
# This list comprehension ensures that self._training_parameters is ordered
# in a way that is consistent with self.feature_map.parameters
self._training_parameters = [
p for p in self._unbound_feature_map.parameters
if (p not in input_params)
]
# Remove param if it was overwritten
if param not in self._training_parameters:
del self._training_parameter_binds[param]
# Add new parameters
for sub_param in bind.parameters:
if sub_param not in self._training_parameter_binds.keys():
self._training_parameter_binds[sub_param] = sub_param
# If parameter is being set to expression of itself, training_parameter_binds
# reflects a self-bind
if param in bind.parameters:
self._training_parameter_binds[param] = param
# If assignment is numerical, update the param_binds
elif isinstance(bind, numbers.Number):
self._training_parameter_binds[param] = bind
else:
raise ValueError(f"""
Parameters can only be bound to numeric values,
Parameters, or ParameterExpressions. Type {type(bind)}
is not supported.
""")
# Reorder dict according to self._training_parameters
self._training_parameter_binds = {
param: self._training_parameter_binds[param]
for param in self._training_parameters
}
# Update feature map with numerical parameter assignments
self._feature_map = self._unbound_feature_map.assign_parameters(
self._training_parameter_binds)
@property
def training_parameter_binds(self) -> Optional[Mapping[Parameter, float]]:
"""Return a copy of the current training parameter mappings for the feature map circuit."""
return copy.deepcopy(self._training_parameter_binds)
def bind_training_parameters(
self, values: Union[Mapping[Parameter, ParameterValueType],
Sequence[ParameterValueType]]
) -> None:
"""
Alternate function signature for ``assign_training_parameters``
"""
self.assign_training_parameters(values)
def get_unbound_training_parameters(self) -> List[Parameter]:
"""Return a list of any unbound training parameters in the feature map circuit."""
unbound_training_params = []
if self._training_parameter_binds is not None:
# Get all training parameters not associated with numerical values
unbound_training_params = [
val for val in self._training_parameter_binds.values()
if not isinstance(val, numbers.Number)
]
return unbound_training_params
@property # type: ignore
@deprecate_property("0.5.0", new_name="training_parameters")
def user_parameters(
self) -> Optional[Union[ParameterVector, Sequence[Parameter]]]:
"""[Deprecated property]Return the vector of training parameters."""
return self.training_parameters
@user_parameters.setter # type: ignore
@deprecate_property("0.5.0", new_name="training_parameters")
def user_parameters(
self, training_params: Union[ParameterVector,
Sequence[Parameter]]) -> None:
"""[Deprecated property setter]Set the training parameters"""
self.training_parameters = training_params
@deprecate_method("0.5.0", new_name="assign_training_parameters")
def assign_user_parameters(
self, values: Union[Mapping[Parameter, ParameterValueType],
Sequence[ParameterValueType]]
) -> None:
"""
[Deprecated method]Assign training parameters in the ``QuantumKernel`` feature map.
Otherwise, just like ``assign_training_parameters``.
"""
self.assign_training_parameters(values)
@property # type: ignore
@deprecate_property("0.5.0", new_name="training_parameter_binds")
def user_param_binds(self) -> Optional[Mapping[Parameter, float]]:
"""
[Deprecated property]Return a copy of the current training parameter mappings
for the feature map circuit.
"""
return self.training_parameter_binds
@deprecate_method("0.5.0", new_name="bind_training_parameters")
def bind_user_parameters(
self, values: Union[Mapping[Parameter, ParameterValueType],
Sequence[ParameterValueType]]
) -> None:
"""
[Deprecated method]Alternate function signature for ``assign_training_parameters``
"""
self.bind_training_parameters(values)
@deprecate_method("0.5.0", new_name="get_unbound_training_parameters")
def get_unbound_user_parameters(self) -> List[Parameter]:
"""
[Deprecated method]Return a list of any unbound training parameters in the feature
map circuit.
"""
return self.get_unbound_training_parameters()
def construct_circuit(
self,
x: ParameterVector,
y: ParameterVector = None,
measurement: bool = True,
is_statevector_sim: bool = False,
) -> QuantumCircuit:
r"""
Construct inner product circuit for given datapoints and feature map.
If using `statevector_simulator`, only construct circuit for :math:`\Psi(x)|0\rangle`,
otherwise construct :math:`Psi^dagger(y) x Psi(x)|0>`
If y is None and not using `statevector_simulator`, self inner product is calculated.
Args:
x: first data point parameter vector
y: second data point parameter vector, ignored if using statevector simulator
measurement: include measurement if not using statevector simulator
is_statevector_sim: use state vector simulator
Returns:
QuantumCircuit
Raises:
ValueError:
- x and/or y have incompatible dimension with feature map
- unbound training parameters in the feature map circuit
"""
# Ensure all training parameters have been bound in the feature map circuit.
unbound_params = self.get_unbound_training_parameters()
if unbound_params:
raise ValueError(f"""
The feature map circuit contains unbound training parameters ({unbound_params}).
All training parameters must be bound to numerical values before constructing
inner product circuit.
""")
if len(x) != self._feature_map.num_parameters:
raise ValueError(
"x and class feature map incompatible dimensions.\n"
f"x has {len(x)} dimensions, but feature map has {self._feature_map.num_parameters}."
)
q = QuantumRegister(self._feature_map.num_qubits, "q")
c = ClassicalRegister(self._feature_map.num_qubits, "c")
qc = QuantumCircuit(q, c)
x_dict = dict(zip(self._feature_map.parameters, x))
psi_x = self._feature_map.assign_parameters(x_dict)
qc.append(psi_x.to_instruction(), qc.qubits)
if not is_statevector_sim:
if y is not None and len(y) != self._feature_map.num_parameters:
raise ValueError(
"y and class feature map incompatible dimensions.\n"
f"y has {len(y)} dimensions, but feature map has {self._feature_map.num_parameters}."
)
if y is None:
y = x
y_dict = dict(zip(self._feature_map.parameters, y))
psi_y_dag = self._feature_map.assign_parameters(y_dict)
qc.append(psi_y_dag.to_instruction().inverse(), qc.qubits)
if measurement:
qc.barrier(q)
qc.measure(q, c)
return qc
def _compute_overlap(self, idx, results, is_statevector_sim,
measurement_basis) -> float:
"""
Helper function to compute overlap for given input.
"""
if is_statevector_sim:
# |<0|Psi^dagger(y) x Psi(x)|0>|^2, take the amplitude
v_a, v_b = [results[int(i)] for i in idx]
tmp = np.vdot(v_a, v_b)
kernel_value = np.vdot(tmp, tmp).real # pylint: disable=no-member
else:
result = results.get_counts(idx)
kernel_value = result.get(measurement_basis, 0) / sum(
result.values())
return kernel_value
def evaluate(self,
x_vec: np.ndarray,
y_vec: np.ndarray = None) -> np.ndarray:
r"""
Construct kernel matrix for given data and feature map
If y_vec is None, self inner product is calculated.
If using `statevector_simulator`, only build circuits for :math:`\Psi(x)|0\rangle`,
then perform inner product classically.
Args:
x_vec: 1D or 2D array of datapoints, NxD, where N is the number of datapoints,
D is the feature dimension
y_vec: 1D or 2D array of datapoints, MxD, where M is the number of datapoints,
D is the feature dimension
Returns:
2D matrix, NxM
Raises:
QiskitMachineLearningError:
- A quantum instance or backend has not been provided
ValueError:
- unbound training parameters in the feature map circuit
- x_vec and/or y_vec are not one or two dimensional arrays
- x_vec and y_vec have have incompatible dimensions
- x_vec and/or y_vec have incompatible dimension with feature map and
and feature map can not be modified to match.
"""
# Ensure all training parameters have been bound in the feature map circuit.
unbound_params = self.get_unbound_training_parameters()
if unbound_params:
raise ValueError(f"""
The feature map circuit contains unbound training parameters ({unbound_params}).
All training parameters must be bound to numerical values before evaluating
the kernel matrix.
""")
if self._quantum_instance is None:
raise QiskitMachineLearningError(
"A QuantumInstance or Backend must be supplied to evaluate a quantum kernel."
)
if isinstance(self._quantum_instance, Backend):
self._quantum_instance = QuantumInstance(self._quantum_instance)
if not isinstance(x_vec, np.ndarray):
x_vec = np.asarray(x_vec)
if y_vec is not None and not isinstance(y_vec, np.ndarray):
y_vec = np.asarray(y_vec)
if x_vec.ndim > 2:
raise ValueError("x_vec must be a 1D or 2D array")
if x_vec.ndim == 1:
x_vec = np.reshape(x_vec, (-1, len(x_vec)))
if y_vec is not None and y_vec.ndim > 2:
raise ValueError("y_vec must be a 1D or 2D array")
if y_vec is not None and y_vec.ndim == 1:
y_vec = np.reshape(y_vec, (-1, len(y_vec)))
if y_vec is not None and y_vec.shape[1] != x_vec.shape[1]:
raise ValueError(
"x_vec and y_vec have incompatible dimensions.\n"
f"x_vec has {x_vec.shape[1]} dimensions, but y_vec has {y_vec.shape[1]}."
)
if x_vec.shape[1] != self._feature_map.num_parameters:
try:
self._feature_map.num_qubits = x_vec.shape[1]
except AttributeError:
raise ValueError(
"x_vec and class feature map have incompatible dimensions.\n"
f"x_vec has {x_vec.shape[1]} dimensions, "
f"but feature map has {self._feature_map.num_parameters}."
) from AttributeError
if y_vec is not None and y_vec.shape[
1] != self._feature_map.num_parameters:
raise ValueError(
"y_vec and class feature map have incompatible dimensions.\n"
f"y_vec has {y_vec.shape[1]} dimensions, but feature map "
f"has {self._feature_map.num_parameters}.")
# determine if calculating self inner product
is_symmetric = True
if y_vec is None:
y_vec = x_vec
elif not np.array_equal(x_vec, y_vec):
is_symmetric = False
# initialize kernel matrix
kernel = np.zeros((x_vec.shape[0], y_vec.shape[0]))
# set diagonal to 1 if symmetric
if is_symmetric:
np.fill_diagonal(kernel, 1)
# get indices to calculate
if is_symmetric:
mus, nus = np.triu_indices(x_vec.shape[0], k=1) # remove diagonal
else:
mus, nus = np.indices((x_vec.shape[0], y_vec.shape[0]))
mus = np.asarray(mus.flat)
nus = np.asarray(nus.flat)
is_statevector_sim = self._quantum_instance.is_statevector
measurement = not is_statevector_sim
measurement_basis = "0" * self._feature_map.num_qubits
# calculate kernel
if is_statevector_sim: # using state vector simulator
if is_symmetric:
to_be_computed_data = x_vec
else: # not symmetric
to_be_computed_data = np.concatenate((x_vec, y_vec))
feature_map_params = ParameterVector(
"par_x", self._feature_map.num_parameters)
parameterized_circuit = self.construct_circuit(
feature_map_params,
feature_map_params,
measurement=measurement,
is_statevector_sim=is_statevector_sim,
)
parameterized_circuit = self._quantum_instance.transpile(
parameterized_circuit,
pass_manager=self._quantum_instance.unbound_pass_manager)[0]
statevectors = []
for min_idx in range(0, len(to_be_computed_data),
self._batch_size):
max_idx = min(min_idx + self._batch_size,
len(to_be_computed_data))
circuits = [
parameterized_circuit.assign_parameters(
{feature_map_params: x})
for x in to_be_computed_data[min_idx:max_idx]
]
if self._quantum_instance.bound_pass_manager is not None:
circuits = self._quantum_instance.transpile(
circuits,
pass_manager=self._quantum_instance.bound_pass_manager)
results = self._quantum_instance.execute(circuits,
had_transpiled=True)
for j in range(max_idx - min_idx):
statevectors.append(results.get_statevector(j))
offset = 0 if is_symmetric else len(x_vec)
matrix_elements = [
self._compute_overlap(idx, statevectors, is_statevector_sim,
measurement_basis)
for idx in list(zip(mus, nus + offset))
]
for i, j, value in zip(mus, nus, matrix_elements):
kernel[i, j] = value
if is_symmetric:
kernel[j, i] = kernel[i, j]
else: # not using state vector simulator
feature_map_params_x = ParameterVector(
"par_x", self._feature_map.num_parameters)
feature_map_params_y = ParameterVector(
"par_y", self._feature_map.num_parameters)
parameterized_circuit = self.construct_circuit(
feature_map_params_x,
feature_map_params_y,
measurement=measurement,
is_statevector_sim=is_statevector_sim,
)
parameterized_circuit = self._quantum_instance.transpile(
parameterized_circuit,
pass_manager=self._quantum_instance.unbound_pass_manager)[0]
for idx in range(0, len(mus), self._batch_size):
to_be_computed_data_pair = []
to_be_computed_index = []
for sub_idx in range(idx, min(idx + self._batch_size,
len(mus))):
i = mus[sub_idx]
j = nus[sub_idx]
x_i = x_vec[i]
y_j = y_vec[j]
if not np.all(x_i == y_j):
to_be_computed_data_pair.append((x_i, y_j))
to_be_computed_index.append((i, j))
circuits = [
parameterized_circuit.assign_parameters({
feature_map_params_x:
x,
feature_map_params_y:
y
}) for x, y in to_be_computed_data_pair
]
if self._quantum_instance.bound_pass_manager is not None:
circuits = self._quantum_instance.transpile(
circuits,
pass_manager=self._quantum_instance.bound_pass_manager)
results = self._quantum_instance.execute(circuits,
had_transpiled=True)
matrix_elements = [
self._compute_overlap(circuit, results, is_statevector_sim,
measurement_basis)
for circuit in range(len(circuits))
]
for (i, j), value in zip(to_be_computed_index,
matrix_elements):
kernel[i, j] = value
if is_symmetric:
kernel[j, i] = kernel[i, j]
if self._enforce_psd and is_symmetric:
# Find the closest positive semi-definite approximation to symmetric kernel matrix.
# The (symmetric) matrix should always be positive semi-definite by construction,
# but this can be violated in case of noise, such as sampling noise, thus the
# adjustment is only done if NOT using the statevector simulation.
D, U = np.linalg.eig(kernel) # pylint: disable=invalid-name
kernel = U @ np.diag(np.maximum(0, D)) @ U.transpose()
return kernel
def get_kernel_matrix(quantum_instance: QuantumInstance,
feature_map: QuantumCircuit,
x1_vec: np.ndarray,
x2_vec: Optional[np.ndarray] = None,
enforce_psd: bool = True) -> np.ndarray:
"""
Construct kernel matrix, if x2_vec is None, self-innerproduct is conducted.
Notes:
When using `statevector_simulator`,
we only build the circuits for Psi(x1)|0> rather than
Psi(x2)^dagger Psi(x1)|0>, and then we perform the inner product classically.
That is, for `statevector_simulator`,
the total number of circuits will be O(N) rather than
O(N^2) for `qasm_simulator`.
Args:
quantum_instance: quantum backend with all settings
feature_map: a feature map that maps data to feature space
x1_vec: data points, 2-D array, N1xD, where N1 is the number of data,
D is the feature dimension
x2_vec: data points, 2-D array, N2xD, where N2 is the number of data,
D is the feature dimension
enforce_psd: enforces that the kernel matrix is positive semi-definite by setting
negative eigenvalues to zero. This is only applied in the symmetric
case, i.e., if `x2_vec == None`.
Returns:
2-D matrix, N1xN2
"""
use_parameterized_circuits = True
if x2_vec is None:
is_symmetric = True
x2_vec = x1_vec
else:
is_symmetric = False
is_statevector_sim = quantum_instance.is_statevector
measurement = not is_statevector_sim
measurement_basis = '0' * feature_map.num_qubits
mat = np.ones((x1_vec.shape[0], x2_vec.shape[0]))
# get all indices
if is_symmetric:
mus, nus = np.triu_indices(x1_vec.shape[0],
k=1) # remove diagonal term
else:
mus, nus = np.indices((x1_vec.shape[0], x2_vec.shape[0]))
mus = np.asarray(mus.flat)
nus = np.asarray(nus.flat)
if is_statevector_sim:
if is_symmetric:
to_be_computed_data = x1_vec
else:
to_be_computed_data = np.concatenate((x1_vec, x2_vec))
if use_parameterized_circuits:
# build parameterized circuits, it could be slower for building circuit
# but overall it should be faster since it only transpile one circuit
feature_map_params = ParameterVector(
'x', feature_map.feature_dimension)
parameterized_circuit = QSVM._construct_circuit(
(feature_map_params, feature_map_params),
feature_map,
measurement,
is_statevector_sim=is_statevector_sim)
parameterized_circuit = quantum_instance.transpile(
parameterized_circuit)[0]
circuits = [
parameterized_circuit.assign_parameters(
{feature_map_params: x}) for x in to_be_computed_data
]
else:
# the second x is redundant
to_be_computed_data_pair = [(x, x)
for x in to_be_computed_data]
if logger.isEnabledFor(logging.DEBUG):
logger.debug("Building circuits:")
TextProgressBar(sys.stderr)
circuits = parallel_map(
QSVM._construct_circuit,
to_be_computed_data_pair,
task_args=(feature_map, measurement, is_statevector_sim),
num_processes=algorithm_globals.num_processes)
results = quantum_instance.execute(
circuits, had_transpiled=use_parameterized_circuits)
if logger.isEnabledFor(logging.DEBUG):
logger.debug("Calculating overlap:")
TextProgressBar(sys.stderr)
offset = 0 if is_symmetric else len(x1_vec)
matrix_elements = parallel_map(
QSVM._compute_overlap,
list(zip(mus, nus + offset)),
task_args=(results, is_statevector_sim, measurement_basis),
num_processes=algorithm_globals.num_processes)
for i, j, value in zip(mus, nus, matrix_elements):
mat[i, j] = value
if is_symmetric:
mat[j, i] = mat[i, j]
else:
for idx in range(0, len(mus), QSVM.BATCH_SIZE):
to_be_computed_data_pair = []
to_be_computed_index = []
for sub_idx in range(idx, min(idx + QSVM.BATCH_SIZE,
len(mus))):
i = mus[sub_idx]
j = nus[sub_idx]
x1 = x1_vec[i]
x2 = x2_vec[j]
if not np.all(x1 == x2):
to_be_computed_data_pair.append((x1, x2))
to_be_computed_index.append((i, j))
if use_parameterized_circuits:
# build parameterized circuits, it could be slower for building circuit
# but overall it should be faster since it only transpile one circuit
feature_map_params_x = ParameterVector(
'x', feature_map.feature_dimension)
feature_map_params_y = ParameterVector(
'y', feature_map.feature_dimension)
parameterized_circuit = QSVM._construct_circuit(
(feature_map_params_x, feature_map_params_y),
feature_map,
measurement,
is_statevector_sim=is_statevector_sim)
parameterized_circuit = quantum_instance.transpile(
parameterized_circuit)[0]
circuits = [
parameterized_circuit.assign_parameters({
feature_map_params_x:
x,
feature_map_params_y:
y
}) for x, y in to_be_computed_data_pair
]
else:
if logger.isEnabledFor(logging.DEBUG):
logger.debug("Building circuits:")
TextProgressBar(sys.stderr)
circuits = parallel_map(
QSVM._construct_circuit,
to_be_computed_data_pair,
task_args=(feature_map, measurement),
num_processes=algorithm_globals.num_processes)
results = quantum_instance.execute(
circuits, had_transpiled=use_parameterized_circuits)
if logger.isEnabledFor(logging.DEBUG):
logger.debug("Calculating overlap:")
TextProgressBar(sys.stderr)
matrix_elements = parallel_map(
QSVM._compute_overlap,
range(len(circuits)),
task_args=(results, is_statevector_sim, measurement_basis),
num_processes=algorithm_globals.num_processes)
for (i, j), value in zip(to_be_computed_index,
matrix_elements):
mat[i, j] = value
if is_symmetric:
mat[j, i] = mat[i, j]
if enforce_psd and is_symmetric and not is_statevector_sim:
# Find the closest positive semi-definite approximation to kernel matrix, in case it is
# symmetric. The (symmetric) matrix should always be positive semi-definite by
# construction, but this can be violated in case of noise, such as sampling noise, thus,
# the adjustment is only done if NOT using the statevector simulation.
D, U = np.linalg.eig(mat)
mat = U @ np.diag(np.maximum(0, D)) @ U.transpose()
return mat
class QuantumKernel:
r"""Quantum Kernel.
The general task of machine learning is to find and study patterns in data. For many
algorithms, the datapoints are better understood in a higher dimensional feature space,
through the use of a kernel function:
.. math::
K(x, y) = \langle f(x), f(y)\rangle.
Here K is the kernel function, x, y are n dimensional inputs. f is a map from n-dimension
to m-dimension space. :math:`\langle x, y \rangle` denotes the dot product.
Usually m is much larger than n.
The quantum kernel algorithm calculates a kernel matrix, given datapoints x and y and feature
map f, all of n dimension. This kernel matrix can then be used in classical machine learning
algorithms such as support vector classification, spectral clustering or ridge regression.
"""
def __init__(self,
feature_map: Optional[QuantumCircuit] = None,
enforce_psd: bool = True,
batch_size: int = 1000,
quantum_instance: Optional[
Union[QuantumInstance, BaseBackend, Backend]] = None) -> None:
"""
Args:
feature_map: Parameterized circuit to be used as the feature map. If None is given,
the `ZZFeatureMap` is used with two qubits.
enforce_psd: Project to closest positive semidefinite matrix if x = y.
Only enforced when not using the state vector simulator. Default True.
batch_size: Number of circuits to batch together for computation. Default 1000.
quantum_instance: Quantum Instance or Backend
"""
self._feature_map = feature_map if feature_map else ZZFeatureMap(2)
self._enforce_psd = enforce_psd
self._batch_size = batch_size
self._quantum_instance = quantum_instance
@property
def feature_map(self) -> QuantumCircuit:
""" Returns feature map """
return self._feature_map
@feature_map.setter
def feature_map(self, feature_map: QuantumCircuit):
""" Sets feature map """
self._feature_map = feature_map
@property
def quantum_instance(self) -> QuantumInstance:
""" Returns quantum instance """
return self._quantum_instance
@quantum_instance.setter
def quantum_instance(self, quantum_instance: Union[Backend,
BaseBackend, QuantumInstance]) -> None:
""" Sets quantum instance """
if isinstance(quantum_instance, (BaseBackend, Backend)):
self._quantum_instance = QuantumInstance(quantum_instance)
else:
self._quantum_instance = quantum_instance
def construct_circuit(self, x: ParameterVector, y: ParameterVector = None,
measurement: bool = True,
is_statevector_sim: bool = False) -> QuantumCircuit:
r"""
Construct inner product circuit for given datapoints and feature map.
If using `statevector_simulator`, only construct circuit for :math:`\Psi(x)|0\rangle`,
otherwise construct :math:`Psi^dagger(y) x Psi(x)|0>`
If y is None and not using `statevector_simulator`, self inner product is calculated.
Args:
x: first data point parameter vector
y: second data point parameter vector, ignored if using statevector simulator
measurement: include measurement if not using statevector simulator
is_statevector_sim: use state vector simulator
Returns:
QuantumCircuit
Raises:
ValueError:
- x and/or y have incompatible dimension with feature map
"""
if len(x) != self._feature_map.num_parameters:
raise ValueError("x and class feature map incompatible dimensions.\n" +
"x has %s dimensions, but feature map has %s." %
(len(x), self._feature_map.num_parameters))
q = QuantumRegister(self._feature_map.num_qubits, 'q')
c = ClassicalRegister(self._feature_map.num_qubits, 'c')
qc = QuantumCircuit(q, c)
x_dict = dict(zip(self._feature_map.parameters, x))
psi_x = self._feature_map.assign_parameters(x_dict)
qc.append(psi_x.to_instruction(), qc.qubits)
if not is_statevector_sim:
if y is not None and len(y) != self._feature_map.num_parameters:
raise ValueError("y and class feature map incompatible dimensions.\n" +
"y has %s dimensions, but feature map has %s." %
(len(y), self._feature_map.num_parameters))
if y is None:
y = x
y_dict = dict(zip(self._feature_map.parameters, y))
psi_y_dag = self._feature_map.assign_parameters(y_dict)
qc.append(psi_y_dag.to_instruction().inverse(), qc.qubits)
if measurement:
qc.barrier(q)
qc.measure(q, c)
return qc
def _compute_overlap(self, idx, results, is_statevector_sim, measurement_basis):
"""
Helper function to compute overlap for given input.
"""
if is_statevector_sim:
# |<0|Psi^dagger(y) x Psi(x)|0>|^2, take the amplitude
v_a, v_b = [results.get_statevector(int(i)) for i in idx]
tmp = np.vdot(v_a, v_b)
kernel_value = np.vdot(tmp, tmp).real # pylint: disable=no-member
else:
result = results.get_counts(idx)
kernel_value = result.get(measurement_basis, 0) / sum(result.values())
return kernel_value
def evaluate(self, x_vec: np.ndarray, y_vec: np.ndarray = None) -> np.ndarray:
r"""
Construct kernel matrix for given data and feature map
If y_vec is None, self inner product is calculated.
If using `statevector_simulator`, only build circuits for :math:`\Psi(x)|0\rangle`,
then perform inner product classically.
Args:
x_vec: 1D or 2D array of datapoints, NxD, where N is the number of datapoints,
D is the feature dimension
y_vec: 1D or 2D array of datapoints, MxD, where M is the number of datapoints,
D is the feature dimension
Returns:
2D matrix, NxM
Raises:
QiskitMachineLearningError:
- A quantum instance or backend has not been provided
ValueError:
- x_vec and/or y_vec are not one or two dimensional arrays
- x_vec and y_vec have have incompatible dimensions
- x_vec and/or y_vec have incompatible dimension with feature map and
and feature map can not be modified to match.
"""
if self._quantum_instance is None:
raise QiskitMachineLearningError(
"A QuantumInstance or Backend must be supplied to evaluate a quantum kernel.")
if isinstance(self._quantum_instance, (BaseBackend, Backend)):
self._quantum_instance = QuantumInstance(self._quantum_instance)
if not isinstance(x_vec, np.ndarray):
x_vec = np.asarray(x_vec)
if y_vec is not None and not isinstance(y_vec, np.ndarray):
y_vec = np.asarray(y_vec)
if x_vec.ndim > 2:
raise ValueError("x_vec must be a 1D or 2D array")
if x_vec.ndim == 1:
x_vec = np.reshape(x_vec, (-1, 2))
if y_vec is not None and y_vec.ndim > 2:
raise ValueError("y_vec must be a 1D or 2D array")
if y_vec is not None and y_vec.ndim == 1:
y_vec = np.reshape(y_vec, (-1, 2))
if y_vec is not None and y_vec.shape[1] != x_vec.shape[1]:
raise ValueError("x_vec and y_vec have incompatible dimensions.\n" +
"x_vec has %s dimensions, but y_vec has %s." %
(x_vec.shape[1], y_vec.shape[1]))
if x_vec.shape[1] != self._feature_map.num_parameters:
try:
self._feature_map.num_qubits = x_vec.shape[1]
except AttributeError:
raise ValueError(
"x_vec and class feature map have incompatible dimensions.\n" +
"x_vec has %s dimensions, but feature map has %s." %
(x_vec.shape[1], self._feature_map.num_parameters)) from AttributeError
if y_vec is not None and y_vec.shape[1] != self._feature_map.num_parameters:
raise ValueError("y_vec and class feature map have incompatible dimensions.\n" +
"y_vec has %s dimensions, but feature map has %s." %
(y_vec.shape[1], self._feature_map.num_parameters))
# determine if calculating self inner product
is_symmetric = True
if y_vec is None:
y_vec = x_vec
elif not np.array_equal(x_vec, y_vec):
is_symmetric = False
# initialize kernel matrix
kernel = np.zeros((x_vec.shape[0], y_vec.shape[0]))
# set diagonal to 1 if symmetric
if is_symmetric:
np.fill_diagonal(kernel, 1)
# get indices to calculate
if is_symmetric:
mus, nus = np.triu_indices(x_vec.shape[0], k=1) # remove diagonal
else:
mus, nus = np.indices((x_vec.shape[0], y_vec.shape[0]))
mus = np.asarray(mus.flat)
nus = np.asarray(nus.flat)
is_statevector_sim = self._quantum_instance.is_statevector
measurement = not is_statevector_sim
measurement_basis = '0' * self._feature_map.num_qubits
# calculate kernel
if is_statevector_sim: # using state vector simulator
if is_symmetric:
to_be_computed_data = x_vec
else: # not symmetric
to_be_computed_data = np.concatenate((x_vec, y_vec))
feature_map_params = ParameterVector('par_x', self._feature_map.num_parameters)
parameterized_circuit = self.construct_circuit(
feature_map_params, feature_map_params,
measurement=measurement, is_statevector_sim=is_statevector_sim)
parameterized_circuit = self._quantum_instance.transpile(parameterized_circuit)[0]
circuits = [parameterized_circuit.assign_parameters({feature_map_params: x})
for x in to_be_computed_data]
results = self._quantum_instance.execute(circuits)
offset = 0 if is_symmetric else len(x_vec)
matrix_elements = [self._compute_overlap(idx, results,
is_statevector_sim, measurement_basis)
for idx in list(zip(mus, nus + offset))]
for i, j, value in zip(mus, nus, matrix_elements):
kernel[i, j] = value
if is_symmetric:
kernel[j, i] = kernel[i, j]
else: # not using state vector simulator
feature_map_params_x = ParameterVector('par_x', self._feature_map.num_parameters)
feature_map_params_y = ParameterVector('par_y', self._feature_map.num_parameters)
parameterized_circuit = self.construct_circuit(
feature_map_params_x, feature_map_params_y,
measurement=measurement, is_statevector_sim=is_statevector_sim)
parameterized_circuit = self._quantum_instance.transpile(parameterized_circuit)[0]
for idx in range(0, len(mus), self._batch_size):
to_be_computed_data_pair = []
to_be_computed_index = []
for sub_idx in range(idx, min(idx + self._batch_size, len(mus))):
i = mus[sub_idx]
j = nus[sub_idx]
x_i = x_vec[i]
y_j = y_vec[j]
if not np.all(x_i == y_j):
to_be_computed_data_pair.append((x_i, y_j))
to_be_computed_index.append((i, j))
circuits = [parameterized_circuit.assign_parameters({feature_map_params_x: x,
feature_map_params_y: y})
for x, y in to_be_computed_data_pair]
results = self._quantum_instance.execute(circuits)
matrix_elements = [self._compute_overlap(circuit, results,
is_statevector_sim, measurement_basis)
for circuit in range(len(circuits))]
for (i, j), value in zip(to_be_computed_index, matrix_elements):
kernel[i, j] = value
if is_symmetric:
kernel[j, i] = kernel[i, j]
if self._enforce_psd and is_symmetric:
# Find the closest positive semi-definite approximation to symmetric kernel matrix.
# The (symmetric) matrix should always be positive semi-definite by construction,
# but this can be violated in case of noise, such as sampling noise, thus the
# adjustment is only done if NOT using the statevector simulation.
D, U = np.linalg.eig(kernel) # pylint: disable=invalid-name
kernel = U @ np.diag(np.maximum(0, D)) @ U.transpose()
return kernel