qiskit.aqua.algorithms.QSVM
class QSVM(feature_map, training_dataset=None, test_dataset=None, datapoints=None, multiclass_extension=None, lambda2=0.001, quantum_instance=None)
Quantum SVM algorithm.
A key concept in classification methods is that of a kernel. Data cannot typically be separated by a hyperplane in its original space. A common technique used to find such a hyperplane consists on applying a non-linear transformation function to the data. This function is called a feature map, as it transforms the raw features, or measurable properties, of the phenomenon or subject under study. Classifying in this new feature space – and, as a matter of fact, also in any other space, including the raw original one – is nothing more than seeing how close data points are to each other. This is the same as computing the inner product for each pair of data in the set. In fact we do not need to compute the non-linear feature map for each datum, but only the inner product of each pair of data points in the new feature space. This collection of inner products is called the kernel and it is perfectly possible to have feature maps that are hard to compute but whose kernels are not.
The QSVM algorithm applies to classification problems that require a feature map for which computing the kernel is not efficient classically. This means that the required computational resources are expected to scale exponentially with the size of the problem. QSVM uses a Quantum processor to solve this problem by a direct estimation of the kernel in the feature space. The method used falls in the category of what is called supervised learning, consisting of a training phase (where the kernel is calculated and the support vectors obtained) and a test or classification phase (where new data without labels is classified according to the solution found in the training phase).
Internally, QSVM will run the binary classification or multiclass classification based on how many classes the data has. If the data has more than 2 classes then a multiclass_extension is required to be supplied. Aqua provides several multiclass_extensions.
See also https://arxiv.org/abs/1804.11326
Parameters
- feature_map (
Union[QuantumCircuit,FeatureMap]) – Feature map module, used to transform data - training_dataset (
Optional[Dict[str,ndarray]]) – Training dataset. - test_dataset (
Optional[Dict[str,ndarray]]) – Testing dataset. - datapoints (
Optional[ndarray]) – Prediction dataset. - multiclass_extension (
Optional[MulticlassExtension]) – If number of classes is greater than 2 then a multiclass scheme must be supplied, in the form of a multiclass extension. - lambda2 (
float) – L2 norm regularization factor - quantum_instance (
Union[QuantumInstance,Backend,BaseBackend,None]) – Quantum Instance or Backend
Raises
AquaError – Multiclass extension not supplied when number of classes > 2
__init__
__init__(feature_map, training_dataset=None, test_dataset=None, datapoints=None, multiclass_extension=None, lambda2=0.001, quantum_instance=None)
Parameters
- feature_map (
Union[QuantumCircuit,FeatureMap]) – Feature map module, used to transform data - training_dataset (
Optional[Dict[str,ndarray]]) – Training dataset. - test_dataset (
Optional[Dict[str,ndarray]]) – Testing dataset. - datapoints (
Optional[ndarray]) – Prediction dataset. - multiclass_extension (
Optional[MulticlassExtension]) – If number of classes is greater than 2 then a multiclass scheme must be supplied, in the form of a multiclass extension. - lambda2 (
float) – L2 norm regularization factor - quantum_instance (
Union[QuantumInstance,Backend,BaseBackend,None]) – Quantum Instance or Backend
Raises
AquaError – Multiclass extension not supplied when number of classes > 2
Methods
__init__(feature_map[, training_dataset, …]) | type feature_mapUnion[QuantumCircuit, FeatureMap] |
construct_circuit(x1, x2[, measurement]) | Generate inner product of x1 and x2 with the given feature map. |
construct_kernel_matrix(x1_vec[, x2_vec, …]) | Construct kernel matrix, if x2_vec is None, self-innerproduct is conducted. |
get_kernel_matrix(quantum_instance, …[, …]) | Construct kernel matrix, if x2_vec is None, self-innerproduct is conducted. |
load_model(file_path) | Load a model from a file path. |
predict(data[, quantum_instance]) | Predict using the svm. |
run([quantum_instance]) | Execute the algorithm with selected backend. |
save_model(file_path) | Save the model to a file path. |
set_backend(backend, **kwargs) | Sets backend with configuration. |
setup_datapoint(datapoints) | Setup data points, if the data were there, they would be overwritten. |
setup_test_data(test_dataset) | Setup test data, if the data were there, they would be overwritten. |
setup_training_data(training_dataset) | Setup training data, if the data were there, they would be overwritten. |
test(data, labels[, quantum_instance]) | Test the svm. |
train(data, labels[, quantum_instance]) | Train the svm. |
Attributes
BATCH_SIZE | |
backend | Returns backend. |
quantum_instance | Returns quantum instance. |
random | Return a numpy random. |
ret | returns result |
backend
Returns backend.
Return type
Union[Backend, BaseBackend]
construct_circuit
construct_circuit(x1, x2, measurement=False)
Generate inner product of x1 and x2 with the given feature map.
The dimension of x1 and x2 must be the same.
Parameters
- x1 (numpy.ndarray) – data points, 1-D array, dimension is D
- x2 (numpy.ndarray) – data points, 1-D array, dimension is D
- measurement (bool) – add measurement gates at the end
Returns
constructed circuit
Return type
construct_kernel_matrix
construct_kernel_matrix(x1_vec, x2_vec=None, quantum_instance=None)
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.
Parameters
- x1_vec (numpy.ndarray) – data points, 2-D array, N1xD, where N1 is the number of data, D is the feature dimension
- x2_vec (numpy.ndarray) – data points, 2-D array, N2xD, where N2 is the number of data, D is the feature dimension
- quantum_instance (QuantumInstance) – quantum backend with all settings
Returns
2-D matrix, N1xN2
Return type
numpy.ndarray
Raises
AquaError – Quantum instance is not present.
get_kernel_matrix
static get_kernel_matrix(quantum_instance, feature_map, x1_vec, x2_vec=None, enforce_psd=True)
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.
Parameters
- quantum_instance (QuantumInstance) – quantum backend with all settings
- feature_map (FeatureMap) – a feature map that maps data to feature space
- x1_vec (numpy.ndarray) – data points, 2-D array, N1xD, where N1 is the number of data, D is the feature dimension
- x2_vec (numpy.ndarray) – data points, 2-D array, N2xD, where N2 is the number of data, D is the feature dimension
- enforce_psd (bool) – 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
Return type
numpy.ndarray
load_model
load_model(file_path)
Load a model from a file path.
Parameters
file_path (str) – the path of the saved model.
predict
predict(data, quantum_instance=None)
Predict using the svm.
Parameters
- data (numpy.ndarray) – NxD array, where N is the number of data, D is the feature dimension.
- quantum_instance (QuantumInstance) – quantum backend with all setting
Returns
predicted labels, Nx1 array
Return type
numpy.ndarray
Raises
AquaError – Quantum instance is not present.
quantum_instance
Returns quantum instance.
Return type
Optional[QuantumInstance]
random
Return a numpy random.
ret
returns result
run
run(quantum_instance=None, **kwargs)
Execute the algorithm with selected backend.
Parameters
- quantum_instance (
Union[QuantumInstance,Backend,BaseBackend,None]) – the experimental setting. - kwargs (dict) – kwargs
Returns
results of an algorithm.
Return type
dict
Raises
AquaError – If a quantum instance or backend has not been provided
save_model
save_model(file_path)
Save the model to a file path.
Parameters
file_path (str) – a path to save the model.
set_backend
set_backend(backend, **kwargs)
Sets backend with configuration.
Return type
None
setup_datapoint
setup_datapoint(datapoints)
Setup data points, if the data were there, they would be overwritten.
Parameters
datapoints (numpy.ndarray) – prediction dataset.
setup_test_data
setup_test_data(test_dataset)
Setup test data, if the data were there, they would be overwritten.
Parameters
test_dataset (dict) – test dataset.
setup_training_data
setup_training_data(training_dataset)
Setup training data, if the data were there, they would be overwritten.
Parameters
training_dataset (dict) – training dataset.
test
test(data, labels, quantum_instance=None)
Test the svm.
Parameters
- data (numpy.ndarray) – NxD array, where N is the number of data, D is the feature dimension.
- labels (numpy.ndarray) – Nx1 array, where N is the number of data
- quantum_instance (QuantumInstance) – quantum backend with all setting
Returns
accuracy
Return type
float
Raises
AquaError – Quantum instance is not present.
train
train(data, labels, quantum_instance=None)
Train the svm.
Parameters
- data (numpy.ndarray) – NxD array, where N is the number of data, D is the feature dimension.
- labels (numpy.ndarray) – Nx1 array, where N is the number of data
- quantum_instance (QuantumInstance) – quantum backend with all setting
Raises
AquaError – Quantum instance is not present.