Source code for qiskit.circuit.library.arithmetic.polynomial_pauli_rotations
# 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.
# pylint: disable=no-member
"""Polynomially controlled Pauli-rotations."""
import warnings
from typing import List, Optional, Dict, Sequence
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
[docs]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(p(i)) |i\rangle |0\rangle + \sin(p(i)) |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``.
"""
[docs] def __init__(
self,
num_state_qubits: Optional[int] = None,
coeffs: Optional[List[float]] = None,
basis: str = "Y",
reverse: bool = False,
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').
reverse: If True, apply the polynomial with the reversed list of qubits
(i.e. q_n as q_0, q_n-1 as q_1, etc).
name: The name of the circuit.
"""
# set default internal parameters
self._coeffs = coeffs or [0, 1]
self._reverse = reverse
if self._reverse is True:
warnings.warn(
"The reverse flag has been deprecated. "
"Use circuit.reverse_bits() to reverse order of qubits.",
DeprecationWarning,
)
# initialize super (after setting coeffs)
super().__init__(num_state_qubits=num_state_qubits, basis=basis, name=name)
@property
def coeffs(self) -> List[float]:
"""The multiplicative factor in the rotation angle of the controlled rotations.
The rotation angles are ``slope * 2^0``, ``slope * 2^1``, ... , ``slope * 2^(n-1)`` where
``n`` is the number of state qubits.
Returns:
The rotation angle common in all controlled rotations.
"""
return self._coeffs
@coeffs.setter
def coeffs(self, coeffs: List[float]) -> None:
"""Set the multiplicative factor of the rotation angles.
Args:
The slope of the rotation angles.
"""
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
@property
def reverse(self) -> bool:
"""Whether to apply the rotations on the reversed list of qubits.
Returns:
True, if the rotations are applied on the reversed list, False otherwise.
"""
return self._reverse
@property
def num_ancilla_qubits(self):
"""Deprecated. Use num_ancillas instead."""
warnings.warn(
"The PolynomialPauliRotations.num_ancilla_qubits property is deprecated "
"as of 0.16.0. It will be removed no earlier than 3 months after the release "
"date. You should use the num_ancillas property instead.",
DeprecationWarning,
stacklevel=2,
)
return self.num_ancillas
def _reset_registers(self, num_state_qubits):
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:
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[Sequence[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 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 = ()
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):
# do not build the circuit if _data is already populated
if self._data is not None:
return
self._data = []
# check whether the configuration is valid
self._check_configuration()
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 = []
if self.reverse:
for i, _ in enumerate(c):
if c[i] > 0:
qr_control.append(qr_state[qr_state.size - i - 1])
else:
for i, _ in enumerate(c):
if c[i] > 0:
qr_control.append(qr_state[i])
# apply controlled rotations
if len(qr_control) > 1:
if self.basis == "x":
circuit.mcrx(rotation_coeffs[c], qr_control, qr_target)
elif self.basis == "y":
circuit.mcry(rotation_coeffs[c], qr_control, qr_target)
else:
circuit.mcrz(rotation_coeffs[c], qr_control, qr_target)
elif len(qr_control) == 1:
if self.basis == "x":
circuit.crx(rotation_coeffs[c], qr_control[0], qr_target)
elif self.basis == "y":
circuit.cry(rotation_coeffs[c], qr_control[0], qr_target)
else:
circuit.crz(rotation_coeffs[c], qr_control[0], qr_target)
self.append(circuit.to_gate(), self.qubits)