squlearn.encoding_circuit.ChebyshevTower

class squlearn.encoding_circuit.ChebyshevTower(num_qubits: int, num_features: int, num_chebyshev: int, alpha: float = 1.0, num_layers: int = 1, rotation_gate: str = 'ry', hadamard_start: bool = True, arrangement: str = 'block', nonlinearity: str = 'arccos')

A feature-map that is based on the Chebyshev Tower encoding.

Example for 4 qubits, a 2 dimensional feature vector, 2 Chebyshev terms per feature, and 2 layers:

(Source code, png, hires.png, pdf)

The encoding gate and the scaling factor can be adjusted by parameters. It is also possible to change the indexing of the features.

Parameters:

• num_qubits (int) – Number of qubits of the ChebyshevTower encoding circuit

• num_features (int) – Dimension of the feature vector

• n_chebyshev (int) – Number of Chebyshev tower terms per feature dimension

• alpha (float) – Scaling factor of Chebyshev tower

• num_layers (int) – Number of layers

• rotation_gate (str) – Rotation gate to use. Either rx, ry or rz (default: ry)

• hadamard_start (bool) – If true, the circuit starts with a layer of Hadamard gates (default: True)

• arrangement (str) – Arrangement of the layers, either block or alternating. block: The features are stacked together, alternating: The features are placed alternately (default: block).

• nonlinearity (str) – Mapping function to use for the feature encoding. Either arccos or arctan (default: arccos)

draw(output: str = None, feature_label: str = 'x', parameter_label: str = 'p', decompose: bool = False, **kwargs) → None

Draws the encoding circuit circuit using the QuantumCircuit.draw() function.

Parameters:

• feature_label (str) – Label for the feature vector (default:”x”).

• parameter_label (str) – Label for the parameter vector (default:”p”).

• decompose (bool) – If True, the circuit is decomposed before printing (default: False).

• kwargs – Additional arguments from Qiskit’s QuantumCircuit.draw() function.

Returns:

Returns the circuit in qiskit QuantumCircuit.draw() format

generate_initial_parameters(seed: int | None = None) → ndarray

Generates random parameters for the encoding circuit

Parameters:

seed (Union[int,None]) – Seed for the random number generator (default: None)

Returns:

The randomly generated parameters

get_circuit(features: ParameterVector | ndarray, parameters: ParameterVector | ndarray = None) → QuantumCircuit

Generates and returns the circuit of the Chebyshev encoding circuit.

Parameters:

• features (Union[ParameterVector,np.ndarray]) – Input vector of the features from which the gate inputs are obtained

• param_vec (Union[ParameterVector,np.ndarray]) – Input vector of the parameters from which the gate inputs are obtained

Returns:

Returns the circuit in Qiskit’s QuantumCircuit format

get_params(deep: bool = True) → dict

Returns hyper-parameters and their values of the Chebyshev Tower encoding

Parameters:

deep (bool) – If True, also the parameters for contained objects are returned (default=True).

Returns:

Dictionary with hyper-parameters and values.

set_params(**kwargs) → ChebyshevTower

Sets value of the encoding circuit hyper-parameters.

Parameters:

params – Hyper-parameters and their values, e.g. num_qubits=2.