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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.","","","\"\"\"Polynomially controlled Pauli-rotations.\"\"\"","","from __future__ import annotations","","from itertools import product","","from qiskit.circuit import QuantumRegister, QuantumCircuit","from qiskit.circuit.exceptions import CircuitError","","from .functional_pauli_rotations import FunctionalPauliRotations","","","def _binomial_coefficients(n):"," \"\"\"Return a dictionary of binomial coefficients",""," Based-on/forked from sympy's binomial_coefficients() function [#]",""," .. [#] https://github.com/sympy/sympy/blob/sympy-1.5.1/sympy/ntheory/multinomial.py"," \"\"\"",""," data = {(0, n): 1, (n, 0): 1}"," temp = 1"," for k in range(1, n // 2 + 1):"," temp = (temp * (n - k + 1)) // k"," data[k, n - k] = data[n - k, k] = temp"," return data","","","def _large_coefficients_iter(m, n):"," \"\"\"Return an iterator of multinomial coefficients",""," Based-on/forked from sympy's multinomial_coefficients_iterator() function [#]",""," .. [#] https://github.com/sympy/sympy/blob/sympy-1.5.1/sympy/ntheory/multinomial.py"," \"\"\""," if m < 2 * n or n == 1:"," coefficients = _multinomial_coefficients(m, n)"," for key, value in coefficients.items():"," yield (key, value)"," else:"," coefficients = _multinomial_coefficients(n, n)"," coefficients_dict = {}"," for key, value in coefficients.items():"," coefficients_dict[tuple(filter(None, key))] = value"," coefficients = coefficients_dict",""," temp = [n] + [0] * (m - 1)"," temp_a = tuple(temp)"," b = tuple(filter(None, temp_a))"," yield (temp_a, coefficients[b])"," if n:"," j = 0 # j will be the leftmost nonzero position"," else:"," j = m"," # enumerate tuples in co-lex order"," while j < m - 1:"," # compute next tuple"," temp_j = temp[j]"," if j:"," temp[j] = 0"," temp[0] = temp_j"," if temp_j > 1:"," temp[j + 1] += 1"," j = 0"," else:"," j += 1"," temp[j] += 1",""," temp[0] -= 1"," temp_a = tuple(temp)"," b = tuple(filter(None, temp_a))"," yield (temp_a, coefficients[b])","","","def _multinomial_coefficients(m, n):"," \"\"\"Return an iterator of multinomial coefficients",""," Based-on/forked from sympy's multinomial_coefficients() function [#]",""," .. [#] https://github.com/sympy/sympy/blob/sympy-1.5.1/sympy/ntheory/multinomial.py"," \"\"\""," if not m:"," if n:"," return {}"," return {(): 1}"," if m == 2:"," return _binomial_coefficients(n)"," if m >= 2 * n and n > 1:"," return dict(_large_coefficients_iter(m, n))"," if n:"," j = 0"," else:"," j = m"," temp = [n] + [0] * (m - 1)"," res = {tuple(temp): 1}"," while j < m - 1:"," temp_j = temp[j]"," if j:"," temp[j] = 0"," temp[0] = temp_j"," if temp_j > 1:"," temp[j + 1] += 1"," j = 0"," start = 1"," v = 0"," else:"," j += 1"," start = j + 1"," v = res[tuple(temp)]"," temp[j] += 1"," for k in range(start, m):"," if temp[k]:"," temp[k] -= 1"," v += res[tuple(temp)]"," temp[k] += 1"," temp[0] -= 1"," res[tuple(temp)] = (v * temp_j) // (n - temp[0])"," return res","","","class PolynomialPauliRotations(FunctionalPauliRotations):"," r\"\"\"A circuit implementing polynomial Pauli rotations.",""," For a polynomial :math:`p(x)`, a basis state :math:`|i\\rangle` and a target qubit"," :math:`|0\\rangle` this operator acts as:",""," .. math::",""," |i\\rangle |0\\rangle \\mapsto \\cos\\left(\\frac{p(i)}{2}\\right) |i\\rangle |0\\rangle"," + \\sin\\left(\\frac{p(i)}{2}\\right) |i\\rangle |1\\rangle",""," Let n be the number of qubits representing the state, d the degree of p(x) and q_i the qubits,"," where q_0 is the least significant qubit. Then for",""," .. math::",""," x = \\sum_{i=0}^{n-1} 2^i q_i,",""," we can write",""," .. math::",""," p(x) = \\sum_{j=0}^{j=d} c_j x^j",""," where :math:`c` are the input coefficients, ``coeffs``."," \"\"\"",""," def __init__("," self,"," num_state_qubits: int | None = None,"," coeffs: list[float] | None = None,"," basis: str = \"Y\","," name: str = \"poly\","," ) -> None:"," \"\"\"Prepare an approximation to a state with amplitudes specified by a polynomial.",""," Args:"," num_state_qubits: The number of qubits representing the state."," coeffs: The coefficients of the polynomial. ``coeffs[i]`` is the coefficient of the"," i-th power of x. Defaults to linear: [0, 1]."," basis: The type of Pauli rotation ('X', 'Y', 'Z')."," name: The name of the circuit."," \"\"\""," # set default internal parameters"," self._coeffs = coeffs or [0, 1]",""," # initialize super (after setting coeffs)"," super().__init__(num_state_qubits=num_state_qubits, basis=basis, name=name)",""," @property"," def coeffs(self) -> list[float]:"," \"\"\"The coefficients of the polynomial.",""," ``coeffs[i]`` is the coefficient of the i-th power of the function input :math:`x`,"," that means that the rotation angles are based on the coefficients value,"," following the formula",""," .. math::",""," c_j x^j , j=0, ..., d",""," where :math:`d` is the degree of the polynomial :math:`p(x)` and :math:`c` are the coefficients"," ``coeffs``.",""," Returns:"," The coefficients of the polynomial."," \"\"\""," return self._coeffs",""," @coeffs.setter"," def coeffs(self, coeffs: list[float]) -> None:"," \"\"\"Set the coefficients of the polynomial.",""," ``coeffs[i]`` is the coefficient of the i-th power of x.",""," Args:"," The coefficients of the polynomial."," \"\"\""," self._invalidate()"," self._coeffs = coeffs",""," @property"," def degree(self) -> int:"," \"\"\"Return the degree of the polynomial, equals to the number of coefficients minus 1.",""," Returns:"," The degree of the polynomial. If the coefficients have not been set, return 0."," \"\"\""," if self.coeffs:"," return len(self.coeffs) - 1"," return 0",""," def _reset_registers(self, num_state_qubits):"," \"\"\"Reset the registers.\"\"\""," if num_state_qubits is not None:"," # set new register of appropriate size"," qr_state = QuantumRegister(num_state_qubits, name=\"state\")"," qr_target = QuantumRegister(1, name=\"target\")",""," self.qregs = [qr_state, qr_target]"," else:"," self.qregs = []",""," def _check_configuration(self, raise_on_failure: bool = True) -> bool:"," \"\"\"Check if the current configuration is valid.\"\"\""," valid = True",""," if self.num_state_qubits is None:"," valid = False"," if raise_on_failure:"," raise AttributeError(\"The number of qubits has not been set.\")",""," if self.num_qubits < self.num_state_qubits + 1:"," valid = False"," if raise_on_failure:"," raise CircuitError("," \"Not enough qubits in the circuit, need at least \""," \"{}.\".format(self.num_state_qubits + 1)"," )",""," return valid",""," def _get_rotation_coefficients(self) -> dict[tuple[int, ...], float]:"," \"\"\"Compute the coefficient of each monomial.",""," Returns:"," A dictionary with pairs ``{control_state: rotation angle}`` where ``control_state``"," is a tuple of ``0`` or ``1`` bits."," \"\"\""," # determine the control states"," all_combinations = list(product([0, 1], repeat=self.num_state_qubits))"," valid_combinations = []"," for combination in all_combinations:"," if 0 < sum(combination) <= self.degree:"," valid_combinations += [combination]",""," rotation_coeffs = {control_state: 0.0 for control_state in valid_combinations}",""," # compute the coefficients for the control states"," for i, coeff in enumerate(self.coeffs[1:]):"," i += 1 # since we skip the first element we need to increase i by one",""," # iterate over the multinomial coefficients"," for comb, num_combs in _multinomial_coefficients(self.num_state_qubits, i).items():"," control_state: tuple[int, ...] = ()"," power = 1"," for j, qubit in enumerate(comb):"," if qubit > 0: # means we control on qubit i"," control_state += (1,)"," power *= 2 ** (j * qubit)"," else:"," control_state += (0,)",""," # Add angle"," rotation_coeffs[control_state] += coeff * num_combs * power",""," return rotation_coeffs",""," def _build(self):"," \"\"\"If not already built, build the circuit.\"\"\""," if self._is_built:"," return",""," super()._build()",""," circuit = QuantumCircuit(*self.qregs, name=self.name)"," qr_state = circuit.qubits[: self.num_state_qubits]"," qr_target = circuit.qubits[self.num_state_qubits]",""," rotation_coeffs = self._get_rotation_coefficients()",""," if self.basis == \"x\":"," circuit.rx(self.coeffs[0], qr_target)"," elif self.basis == \"y\":"," circuit.ry(self.coeffs[0], qr_target)"," else:"," circuit.rz(self.coeffs[0], qr_target)",""," for c in rotation_coeffs:"," qr_control = []"," for i, _ in enumerate(c):"," if c[i] > 0:"," qr_control.append(qr_state[i])",""," # apply controlled 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