squlearn.encoding_circuit.ChebyshevPQC

class squlearn.encoding_circuit.ChebyshevPQC(num_qubits: int, num_layers: int = 1, num_features: int = None, closed: bool = True, entangling_gate: str = 'crz', alpha: float = 4.0, nonlinearity: str = 'arccos')

Chebyshev Encoding Circuit from reference [1].

The encoding circuit consists of three elements:

  1. Basis change in the form of a trainable rotation around the y-axis at start and end.

  2. Non-linear encoding of the features via the Chebyshev polynomials from Rx gates. The degree of the Chebyshev polynomials is optimized during training.

  3. Parameterized two-qubit controlled or RZZ rotations

  1. and 3. form a layer that can be repeated multiple times.

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

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

../../_images/squlearn-encoding_circuit-ChebyshevPQC-1.png

The entangling gate can be chosen between crz and rzz. The latter is more hardware efficient. Also, the entangling between the first and the last qubit can be switched off via the closed parameter to avoid swap gates.

Parameters:

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

  • num_layers (int) – Number of layers of the Chebyshev encoding and the two qubit manipulation (default: 1)

  • num_features (int) – Dimension of the feature vector (default: None)

  • closed (bool) – If false, the last and the first qubit are not entangled (default: True)

  • entangling_gate (str) – Entangling gate to use. Either crz or rzz (default: crz)

  • alpha (float) – Maximum value of the Chebyshev Tower initial parameters, i.e. parameters that appear in the arccos encoding. (default: 4.0)

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

References

[1]: D. A. Kreplin and M. Roth “Reduction of finite sampling noise in quantum neural networks”. arXiv:2306.01639 (2023).

compose(x, concatenate_features=False, concatenate_parameters=False, num_circuit_features: Tuple[int, int] = (None, None))

Composition of encoding circuits with options for handling features and parameters

Number of qubits and features have to be equal in both encoding circuits! The special function and properties of the both encoding circuits are lost by this composition.

Parameters:

  • self (EncodingCircuitBase) – right / first encoding circuit

  • x (EncodingCircuitBase) – left / second encoding circuit

  • concatenate_features (bool) – If True, the features of both encoding circuits are concatenated (default: False). If False, the features of both encoding circuits are taken

  • concatenate_parameters (bool) – If True, the parameters of both encoding circuits are concatenated (default: False). If False, the parameters of both encoding circuits are taken

  • num_circuit_features (Tuple[int, int]) – Tuple of the number of features for both encoding circuits. This has to be provided if concatenate_features is True otherwise an error is raised.

Returns:

Returns the composed encoding circuit as special class ComposedEncodingCircuit

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

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

Parameters:

  • output (str) – Output format of the drawing (default: None).

  • num_features (int) – Number of features to draw the circuit with (default: None).

  • 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.

Raises:

ValueError – Raised if the number of features is not provided.

Returns:

Returns the circuit in qiskit QuantumCircuit.draw() format

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

Generates random parameters for the ChebyshevPQC encoding circuit

Parameters:

  • num_features (int) – Number of features of the input data

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

Returns:

The randomly generated parameters

get_cheb_indices(flatten: bool = True)

Function that returns the indices of the parameters involved in the Chebyshev encoding.

Parameters:

flatten (bool) – If true, the indices are returned as a flat list, otherwise as a list of lists, where the outer list corresponds to the layers (default: True)

get_circuit(features: ParameterVector | ndarray, parameters: ParameterVector | ndarray) → QuantumCircuit

Returns the circuit of the ChebyshevPQC 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_feature_bounds(num_features: int) → ndarray

Returns the feature bounds expanded for a given number of features.

Parameters:

num_features (int) – Number of features to expand the bounds for.

Returns:

Feature bounds expanded for the number of features.

Return type:

np.ndarray

get_params(deep: bool = True) → dict

Returns hyper-parameters and their values of the ChebyshevPQC encoding circuit

Parameters:

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

Returns:

Dictionary with hyper-parameters and values.

inverse()

Returns the inverse of the encoding circuit.

Returns:

The inverse of the encoding circuit

set_params(**kwargs) → ChebyshevPQC

Sets value of the encoding circuit hyper-parameters.

Parameters:

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