squlearn.encoding_circuit.ChebyshevPQC

class squlearn.encoding_circuit.ChebyshevPQC(num_qubits: int, num_features: int, num_layers: int = 1, 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

2. 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)

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_features (int) – Dimension of the feature vector

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

• 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).

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 ChebyshevPQC encoding circuit

Parameters:

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_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.

set_params(**kwargs) → ChebyshevPQC

Sets value of the encoding circuit hyper-parameters.

Parameters:

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