PauliExpansion

class PauliExpansion(feature_dimension, depth=2, entangler_map=None, entanglement='full', paulis=None, data_map_func=<function self_product>)

DEPRECATED. The Pauli Expansion feature map.

Refer to https://arxiv.org/abs/1804.11326 for details.

The Pauli Expansion feature map transforms data $\vec{x} \in \mathbb{R}^n$ according to the following equation, and then duplicate the same circuit with depth $d$ times, where $d$ is the depth of the circuit:

$U_{\Phi(\vec{x})}=\exp\left(i\sum_{S\subseteq [n]} \phi_S(\vec{x})\prod_{i\in S} P_i\right)$

where $S \in \{\binom{n}{k}\ combinations,\ k = 1,... n \}, \phi_S(\vec{x}) = x_i$ if $k=1$, otherwise $\phi_S(\vec{x}) = \prod_S(\pi - x_j)$, where $j \in S$, and $P_i \in \{ I, X, Y, Z \}$

Please refer to FirstOrderExpansion for the case $k = 1$, $P_0 = Z$ and to SecondOrderExpansion for the case $k = 2$, $P_0 = Z\ and\ P_1 P_0 = ZZ$.

Parameters

• feature_dimension (int) – The number of features
• depth (int) – The number of repeated circuits. Defaults to 2, has a minimum value of 1.
• entangler_map (Optional[List[List[int]]]) – Describes the connectivity of qubits, each list in the overall list describes [source, target]. Defaults to None where the map is created as per entanglement parameter. Note that the order in the list is the order of applying the two-qubit gate.
• entanglement (str) – (‘full’ | ‘linear’), generate the qubit connectivity by a predefined topology. Defaults to full which connects every qubit to each other. Linear connects each qubit to the next.
• paulis (Optional[List[str]]) – a list of strings for to-be-used paulis (a pauli is a any combination of I, X, Y ,Z). Note that the order of pauli label is counted from right to left as the notation used in Pauli class in Qiskit Terra. Defaults to None whereupon [‘Z’, ‘ZZ’] will be used.
• data_map_func (Callable[[ndarray], float]) – A mapping function for data x which can be supplied to override the default mapping from self_product().

Attributes

feature_dimension

num_qubits

support_parameterized_circuit

Methods

construct_circuit

get_entangler_map

validate_entangler_map