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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2020.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","","\"\"\"The Pauli expansion circuit module.\"\"\"","","from typing import Optional, Callable, List, Union","from functools import reduce","import numpy as np","","from qiskit.circuit import QuantumCircuit","from qiskit.circuit import Parameter, ParameterVector","from qiskit.circuit.library.standard_gates import HGate","","from ..n_local.n_local import NLocal","","","class PauliFeatureMap(NLocal):"," r\"\"\"The Pauli Expansion circuit.",""," The Pauli Expansion circuit is a data encoding circuit that transforms input data"," :math:`\\vec{x} \\in \\mathbb{R}^n`, where `n` is the ``feature_dimension``, as",""," .. math::",""," U_{\\Phi(\\vec{x})}=\\exp\\left(i\\sum_{S \\in \\mathcal{I}}"," \\phi_S(\\vec{x})\\prod_{i\\in S} P_i\\right).",""," Here, :math:`S` is a set of qubit indices that describes the connections in the feature map,"," :math:`\\mathcal{I}` is a set containing all these index sets, and"," :math:`P_i \\in \\{I, X, Y, Z\\}`. Per default the data-mapping"," :math:`\\phi_S` is",""," .. math::",""," \\phi_S(\\vec{x}) = \\begin{cases}"," x_i \\text{ if } S = \\{i\\} \\\\"," \\prod_{j \\in S} (\\pi - x_j) \\text{ if } |S| > 1"," \\end{cases}.",""," The possible connections can be set using the ``entanglement`` and ``paulis`` arguments."," For example, for single-qubit :math:`Z` rotations and two-qubit :math:`YY` interactions"," between all qubit pairs, we can set::","",""," feature_map = PauliFeatureMap(..., paulis=[\"Z\", \"YY\"], entanglement=\"full\")",""," which will produce blocks of the form",""," .. parsed-literal::",""," ┌───┐┌──────────────┐┌──────────┐ ┌───────────┐"," ┤ H ├┤ U1(2.0*x[0]) ├┤ RX(pi/2) ├──■───────────────────────────────────────■──┤ RX(-pi/2) ├"," ├───┤├──────────────┤├──────────┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐├───────────┤"," ┤ H ├┤ U1(2.0*x[1]) ├┤ RX(pi/2) ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ RX(-pi/2) ├"," └───┘└──────────────┘└──────────┘└───┘└─────────────────────────────────┘└───┘└───────────┘",""," The circuit contains ``reps`` repetitions of this transformation.",""," Please refer to :class:`.ZFeatureMap` for the case of single-qubit Pauli-:math:`Z` rotations"," and to :class:`.ZZFeatureMap` for the single- and two-qubit Pauli-:math:`Z` rotations.",""," Examples:",""," >>> prep = PauliFeatureMap(2, reps=1, paulis=['ZZ'])"," >>> print(prep)"," ┌───┐"," q_0: ┤ H ├──■───────────────────────────────────────■──"," ├───┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐"," q_1: ┤ H ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├"," └───┘└───┘└─────────────────────────────────┘└───┘",""," >>> prep = PauliFeatureMap(2, reps=1, paulis=['Z', 'XX'])"," >>> print(prep)"," ┌───┐┌──────────────┐┌───┐ ┌───┐"," q_0: ┤ H ├┤ U1(2.0*x[0]) ├┤ H ├──■───────────────────────────────────────■──┤ H ├"," ├───┤├──────────────┤├───┤┌─┴─┐┌─────────────────────────────────┐┌─┴─┐├───┤"," q_1: ┤ H ├┤ U1(2.0*x[1]) ├┤ H ├┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├┤ H ├"," └───┘└──────────────┘└───┘└───┘└─────────────────────────────────┘└───┘└───┘",""," >>> prep = PauliFeatureMap(2, reps=1, paulis=['ZY'])"," >>> print(prep)"," ┌───┐┌──────────┐ ┌───────────┐"," q_0: ┤ H ├┤ RX(pi/2) ├──■───────────────────────────────────────■──┤ RX(-pi/2) ├"," ├───┤└──────────┘┌─┴─┐┌─────────────────────────────────┐┌─┴─┐└───────────┘"," q_1: ┤ H ├────────────┤ X ├┤ U1(2.0*(pi - x[0])*(pi - x[1])) ├┤ X ├─────────────"," └───┘ └───┘└─────────────────────────────────┘└───┘",""," >>> from qiskit.circuit.library import EfficientSU2"," >>> prep = PauliFeatureMap(3, reps=3, paulis=['Z', 'YY', 'ZXZ'])"," >>> wavefunction = EfficientSU2(3)"," >>> classifier = prep.compose(wavefunction"," >>> classifier.num_parameters"," 27"," >>> classifier.count_ops()"," OrderedDict([('cx', 39), ('rx', 36), ('u1', 21), ('h', 15), ('ry', 12), ('rz', 12)])",""," References:","","",""," [1] Havlicek et al. Supervised learning with quantum enhanced feature spaces,"," `Nature 567, 209-212 (2019) `__.",""," \"\"\"",""," def __init__("," self,"," feature_dimension: Optional[int] = None,"," reps: int = 2,"," entanglement: Union[str, List[List[int]], Callable[[int], List[int]]] = \"full\","," alpha: float = 2.0,"," paulis: Optional[List[str]] = None,"," data_map_func: Optional[Callable[[np.ndarray], float]] = None,"," parameter_prefix: str = \"x\","," insert_barriers: bool = False,"," name: str = \"PauliFeatureMap\","," ) -> None:"," \"\"\"Create a new Pauli expansion circuit.",""," Args:"," feature_dimension: Number of qubits in the circuit."," reps: The number of repeated circuits."," entanglement: Specifies the entanglement structure. Refer to"," :class:`~qiskit.circuit.library.NLocal` for detail."," alpha: The Pauli rotation factor, multiplicative to the pauli rotations"," paulis: A list of strings for to-be-used paulis. If None are provided, ``['Z', 'ZZ']``"," will be used."," data_map_func: A mapping function for data x which can be supplied to override the"," default mapping from :meth:`self_product`."," parameter_prefix: The prefix used if default parameters are generated."," insert_barriers: If True, barriers are inserted in between the evolution instructions"," and hadamard layers.",""," \"\"\"",""," super().__init__("," num_qubits=feature_dimension,"," reps=reps,"," rotation_blocks=HGate(),"," entanglement=entanglement,"," parameter_prefix=parameter_prefix,"," insert_barriers=insert_barriers,"," skip_final_rotation_layer=True,"," name=name,"," )",""," self._data_map_func = data_map_func or self_product"," self._paulis = paulis or [\"Z\", \"ZZ\"]"," self._alpha = alpha",""," def _parameter_generator("," self, rep: int, block: int, indices: List[int]"," ) -> Optional[List[Parameter]]:"," \"\"\"If certain blocks should use certain parameters this method can be overridden.\"\"\""," params = [self.ordered_parameters[i] for i in indices]"," return params",""," @property"," def num_parameters_settable(self):"," \"\"\"The number of distinct parameters.\"\"\""," return self.feature_dimension",""," @property"," def paulis(self) -> List[str]:"," \"\"\"The Pauli strings used in the entanglement of the qubits.",""," Returns:"," The Pauli strings as list."," \"\"\""," return self._paulis",""," @paulis.setter"," def paulis(self, paulis: List[str]) -> None:"," \"\"\"Set the pauli strings.",""," Args:"," paulis: The new pauli strings."," \"\"\""," self._invalidate()"," self._paulis = paulis",""," @property"," def alpha(self) -> float:"," \"\"\"The Pauli rotation factor (alpha).",""," Returns:"," The Pauli rotation factor."," \"\"\""," return self._alpha",""," @alpha.setter"," def alpha(self, alpha: float) -> None:"," \"\"\"Set the Pauli rotation factor (alpha).",""," Args:"," alpha: Pauli rotation factor"," \"\"\""," self._invalidate()"," self._alpha = alpha",""," @property"," def entanglement_blocks(self):"," return [self.pauli_block(pauli) for pauli in self._paulis]",""," @entanglement_blocks.setter"," def entanglement_blocks(self, entanglement_blocks):"," self._entanglement_blocks = entanglement_blocks",""," @property"," def feature_dimension(self) -> int:"," \"\"\"Returns the feature dimension (which is equal to the number of qubits).",""," Returns:"," The feature dimension of this feature map."," \"\"\""," return self.num_qubits",""," @feature_dimension.setter"," def feature_dimension(self, feature_dimension: int) -> None:"," \"\"\"Set the feature dimension.",""," Args:"," feature_dimension: The new feature dimension."," \"\"\""," self.num_qubits = feature_dimension",""," def _extract_data_for_rotation(self, pauli, x):"," where_non_i = np.where(np.asarray(list(pauli[::-1])) != \"I\")[0]"," x = np.asarray(x)"," return x[where_non_i]",""," def pauli_block(self, pauli_string):"," \"\"\"Get the Pauli block for the feature map circuit.\"\"\""," params = ParameterVector(\"_\", length=len(pauli_string))"," time = self._data_map_func(np.asarray(params))"," return self.pauli_evolution(pauli_string, time)",""," def pauli_evolution(self, pauli_string, time):"," \"\"\"Get the evolution block for the given pauli string.\"\"\""," # for some reason this is in reversed order"," pauli_string = pauli_string[::-1]",""," # trim the pauli string if identities are included"," trimmed = []"," indices = []"," for i, pauli in enumerate(pauli_string):"," if pauli != \"I\":"," trimmed += [pauli]"," indices += [i]",""," evo = QuantumCircuit(len(pauli_string))",""," if len(trimmed) == 0:"," return evo",""," def basis_change(circuit, inverse=False):"," for i, pauli in enumerate(pauli_string):"," if pauli == \"X\":"," circuit.h(i)"," elif pauli == \"Y\":"," circuit.rx(-np.pi / 2 if inverse else np.pi / 2, i)",""," def cx_chain(circuit, inverse=False):"," num_cx = len(indices) - 1"," for i in reversed(range(num_cx)) if inverse else range(num_cx):"," circuit.cx(indices[i], indices[i + 1])",""," basis_change(evo)"," cx_chain(evo)"," evo.p(self.alpha * time, indices[-1])"," cx_chain(evo, inverse=True)"," basis_change(evo, inverse=True)"," return evo","","","def self_product(x: np.ndarray) -> float:"," \"\"\""," Define a function map from R^n to R.",""," Args:"," x: data",""," Returns:"," float: the mapped value"," \"\"\""," coeff = x[0] if len(x) == 1 else reduce(lambda m, n: m * n, np.pi - x)"," return 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