# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2022
#
# 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.
"""
Optimized list of Pauli operators
"""
from collections import defaultdict
import numpy as np
import rustworkx as rx
from qiskit.exceptions import QiskitError
from qiskit.quantum_info.operators.custom_iterator import CustomIterator
from qiskit.quantum_info.operators.mixins import GroupMixin, LinearMixin
from qiskit.quantum_info.operators.symplectic.base_pauli import BasePauli
from qiskit.quantum_info.operators.symplectic.pauli import Pauli
from qiskit.quantum_info.operators.symplectic.pauli_table import PauliTable
from qiskit.quantum_info.operators.symplectic.stabilizer_table import StabilizerTable
[documentos]class PauliList(BasePauli, LinearMixin, GroupMixin):
r"""List of N-qubit Pauli operators.
This class is an efficient representation of a list of
:class:`Pauli` operators. It supports 1D numpy array indexing
returning a :class:`Pauli` for integer indexes or a
:class:`PauliList` for slice or list indices.
**Initialization**
A PauliList object can be initialized in several ways.
``PauliList(list[str])``
where strings are same representation with :class:`~qiskit.quantum_info.Pauli`.
``PauliList(Pauli) and PauliList(list[Pauli])``
where Pauli is :class:`~qiskit.quantum_info.Pauli`.
``PauliList.from_symplectic(z, x, phase)``
where ``z`` and ``x`` are 2 dimensional boolean ``numpy.ndarrays`` and ``phase`` is
an integer in ``[0, 1, 2, 3]``.
For example,
.. code-block::
import numpy as np
from qiskit.quantum_info import Pauli, PauliList
# 1. init from list[str]
pauli_list = PauliList(["II", "+ZI", "-iYY"])
print("1. ", pauli_list)
pauli1 = Pauli("iXI")
pauli2 = Pauli("iZZ")
# 2. init from Pauli
print("2. ", PauliList(pauli1))
# 3. init from list[Pauli]
print("3. ", PauliList([pauli1, pauli2]))
# 4. init from np.ndarray
z = np.array([[True, True], [False, False]])
x = np.array([[False, True], [True, False]])
phase = np.array([0, 1])
pauli_list = PauliList.from_symplectic(z, x, phase)
print("4. ", pauli_list)
.. parsed-literal::
1. ['II', 'ZI', '-iYY']
2. ['iXI']
3. ['iXI', 'iZZ']
4. ['YZ', '-iIX']
**Data Access**
The individual Paulis can be accessed and updated using the ``[]``
operator which accepts integer, lists, or slices for selecting subsets
of PauliList. If integer is given, it returns Pauli not PauliList.
.. code-block::
pauli_list = PauliList(["XX", "ZZ", "IZ"])
print("Integer: ", repr(pauli_list[1]))
print("List: ", repr(pauli_list[[0, 2]]))
print("Slice: ", repr(pauli_list[0:2]))
.. parsed-literal::
Integer: Pauli('ZZ')
List: PauliList(['XX', 'IZ'])
Slice: PauliList(['XX', 'ZZ'])
**Iteration**
Rows in the Pauli table can be iterated over like a list. Iteration can
also be done using the label or matrix representation of each row using the
:meth:`label_iter` and :meth:`matrix_iter` methods.
"""
# Set the max number of qubits * paulis before string truncation
__truncate__ = 2000
def __init__(self, data):
"""Initialize the PauliList.
Args:
data (Pauli or list): input data for Paulis. If input is a list each item in the list
must be a Pauli object or Pauli str.
Raises:
QiskitError: if input array is invalid shape.
Additional Information:
The input array is not copied so multiple Pauli tables
can share the same underlying array.
"""
if isinstance(data, BasePauli):
base_z, base_x, base_phase = data._z, data._x, data._phase
elif isinstance(data, StabilizerTable):
# Conversion from legacy StabilizerTable
base_z, base_x, base_phase = self._from_array(data.Z, data.X, 2 * data.phase)
elif isinstance(data, PauliTable):
# Conversion from legacy PauliTable
base_z, base_x, base_phase = self._from_array(data.Z, data.X)
else:
# Conversion as iterable of Paulis
base_z, base_x, base_phase = self._from_paulis(data)
# Initialize BasePauli
super().__init__(base_z, base_x, base_phase)
# ---------------------------------------------------------------------
# Representation conversions
# ---------------------------------------------------------------------
@property
def settings(self):
"""Return settings."""
return {"data": self.to_labels()}
def __array__(self, dtype=None):
"""Convert to numpy array"""
# pylint: disable=unused-argument
shape = (len(self),) + 2 * (2**self.num_qubits,)
ret = np.zeros(shape, dtype=complex)
for i, mat in enumerate(self.matrix_iter()):
ret[i] = mat
return ret
@staticmethod
def _from_paulis(data):
"""Construct a PauliList from a list of Pauli data.
Args:
data (iterable): list of Pauli data.
Returns:
PauliList: the constructed PauliList.
Raises:
QiskitError: If the input list is empty or contains invalid
Pauli strings.
"""
if not isinstance(data, (list, tuple, set, np.ndarray)):
data = [data]
num_paulis = len(data)
if num_paulis == 0:
raise QiskitError("Input Pauli list is empty.")
paulis = []
for i in data:
if not isinstance(i, Pauli):
paulis.append(Pauli(i))
else:
paulis.append(i)
num_qubits = paulis[0].num_qubits
base_z = np.zeros((num_paulis, num_qubits), dtype=bool)
base_x = np.zeros((num_paulis, num_qubits), dtype=bool)
base_phase = np.zeros(num_paulis, dtype=int)
for i, pauli in enumerate(paulis):
if pauli.num_qubits != num_qubits:
raise ValueError(
f"The {i}th Pauli is defined over {pauli.num_qubits} qubits, "
f"but num_qubits == {num_qubits} was expected."
)
base_z[i] = pauli._z
base_x[i] = pauli._x
base_phase[i] = pauli._phase
return base_z, base_x, base_phase
def __repr__(self):
"""Display representation."""
return self._truncated_str(True)
def __str__(self):
"""Print representation."""
return self._truncated_str(False)
def _truncated_str(self, show_class):
stop = self._num_paulis
if self.__truncate__ and self.num_qubits > 0:
max_paulis = self.__truncate__ // self.num_qubits
if self._num_paulis > max_paulis:
stop = max_paulis
labels = [str(self[i]) for i in range(stop)]
prefix = "PauliList(" if show_class else ""
tail = ")" if show_class else ""
if stop != self._num_paulis:
suffix = ", ...]" + tail
else:
suffix = "]" + tail
list_str = np.array2string(
np.array(labels), threshold=stop + 1, separator=", ", prefix=prefix, suffix=suffix
)
return prefix + list_str[:-1] + suffix
def __eq__(self, other):
"""Entrywise comparison of Pauli equality."""
if not isinstance(other, PauliList):
other = PauliList(other)
if not isinstance(other, BasePauli):
return False
return self._eq(other)
[documentos] def equiv(self, other):
"""Entrywise comparison of Pauli equivalence up to global phase.
Args:
other (PauliList or Pauli): a comparison object.
Returns:
np.ndarray: An array of ``True`` or ``False`` for entrywise equivalence
of the current table.
"""
if not isinstance(other, PauliList):
other = PauliList(other)
return np.all(self.z == other.z, axis=1) & np.all(self.x == other.x, axis=1)
# ---------------------------------------------------------------------
# Direct array access
# ---------------------------------------------------------------------
@property
def phase(self):
"""Return the phase exponent of the PauliList."""
# Convert internal ZX-phase convention to group phase convention
return np.mod(self._phase - self._count_y(dtype=self._phase.dtype), 4)
@phase.setter
def phase(self, value):
# Convert group phase convetion to internal ZX-phase convention
self._phase[:] = np.mod(value + self._count_y(dtype=self._phase.dtype), 4)
@property
def x(self):
"""The x array for the symplectic representation."""
return self._x
@x.setter
def x(self, val):
self._x[:] = val
@property
def z(self):
"""The z array for the symplectic representation."""
return self._z
@z.setter
def z(self, val):
self._z[:] = val
# ---------------------------------------------------------------------
# Size Properties
# ---------------------------------------------------------------------
@property
def shape(self):
"""The full shape of the :meth:`array`"""
return self._num_paulis, self.num_qubits
@property
def size(self):
"""The number of Pauli rows in the table."""
return self._num_paulis
def __len__(self):
"""Return the number of Pauli rows in the table."""
return self._num_paulis
# ---------------------------------------------------------------------
# Pauli Array methods
# ---------------------------------------------------------------------
def __getitem__(self, index):
"""Return a view of the PauliList."""
# Returns a view of specified rows of the PauliList
# This supports all slicing operations the underlying array supports.
if isinstance(index, tuple):
if len(index) == 1:
index = index[0]
elif len(index) > 2:
raise IndexError(f"Invalid PauliList index {index}")
# Row-only indexing
if isinstance(index, (int, np.integer)):
# Single Pauli
return Pauli(
BasePauli(
self._z[np.newaxis, index],
self._x[np.newaxis, index],
self._phase[np.newaxis, index],
)
)
elif isinstance(index, (slice, list, np.ndarray)):
# Sub-Table view
return PauliList(BasePauli(self._z[index], self._x[index], self._phase[index]))
# Row and Qubit indexing
return PauliList((self._z[index], self._x[index], 0))
def __setitem__(self, index, value):
"""Update PauliList."""
if isinstance(index, tuple):
if len(index) == 1:
index = index[0]
elif len(index) > 2:
raise IndexError(f"Invalid PauliList index {index}")
# Modify specified rows of the PauliList
if not isinstance(value, PauliList):
value = PauliList(value)
self._z[index] = value._z
self._x[index] = value._x
if not isinstance(index, tuple):
# Row-only indexing
self._phase[index] = value._phase
else:
# Row and Qubit indexing
self._phase[index[0]] += value._phase
self._phase %= 4
[documentos] def delete(self, ind, qubit=False):
"""Return a copy with Pauli rows deleted from table.
When deleting qubits the qubit index is the same as the
column index of the underlying :attr:`X` and :attr:`Z` arrays.
Args:
ind (int or list): index(es) to delete.
qubit (bool): if ``True`` delete qubit columns, otherwise delete
Pauli rows (Default: ``False``).
Returns:
PauliList: the resulting table with the entries removed.
Raises:
QiskitError: if ``ind`` is out of bounds for the array size or
number of qubits.
"""
if isinstance(ind, int):
ind = [ind]
# Row deletion
if not qubit:
if max(ind) >= len(self):
raise QiskitError(
"Indices {} are not all less than the size"
" of the PauliList ({})".format(ind, len(self))
)
z = np.delete(self._z, ind, axis=0)
x = np.delete(self._x, ind, axis=0)
phase = np.delete(self._phase, ind)
return PauliList(BasePauli(z, x, phase))
# Column (qubit) deletion
if max(ind) >= self.num_qubits:
raise QiskitError(
"Indices {} are not all less than the number of"
" qubits in the PauliList ({})".format(ind, self.num_qubits)
)
z = np.delete(self._z, ind, axis=1)
x = np.delete(self._x, ind, axis=1)
# Use self.phase, not self._phase as deleting qubits can change the
# ZX phase convention
return PauliList.from_symplectic(z, x, self.phase)
[documentos] def insert(self, ind, value, qubit=False):
"""Insert Paulis into the table.
When inserting qubits the qubit index is the same as the
column index of the underlying :attr:`X` and :attr:`Z` arrays.
Args:
ind (int): index to insert at.
value (PauliList): values to insert.
qubit (bool): if ``True`` insert qubit columns, otherwise insert
Pauli rows (Default: ``False``).
Returns:
PauliList: the resulting table with the entries inserted.
Raises:
QiskitError: if the insertion index is invalid.
"""
if not isinstance(ind, int):
raise QiskitError("Insert index must be an integer.")
if not isinstance(value, PauliList):
value = PauliList(value)
# Row insertion
size = self._num_paulis
if not qubit:
if ind > size:
raise QiskitError(
"Index {} is larger than the number of rows in the"
" PauliList ({}).".format(ind, size)
)
base_z = np.insert(self._z, ind, value._z, axis=0)
base_x = np.insert(self._x, ind, value._x, axis=0)
base_phase = np.insert(self._phase, ind, value._phase)
return PauliList(BasePauli(base_z, base_x, base_phase))
# Column insertion
if ind > self.num_qubits:
raise QiskitError(
"Index {} is greater than number of qubits"
" in the PauliList ({})".format(ind, self.num_qubits)
)
if len(value) == 1:
# Pad blocks to correct size
value_x = np.vstack(size * [value.x])
value_z = np.vstack(size * [value.z])
value_phase = np.vstack(size * [value.phase])
elif len(value) == size:
# Blocks are already correct size
value_x = value.x
value_z = value.z
value_phase = value.phase
else:
# Blocks are incorrect size
raise QiskitError(
"Input PauliList must have a single row, or"
" the same number of rows as the Pauli Table"
" ({}).".format(size)
)
# Build new array by blocks
z = np.hstack([self.z[:, :ind], value_z, self.z[:, ind:]])
x = np.hstack([self.x[:, :ind], value_x, self.x[:, ind:]])
phase = self.phase + value_phase
return PauliList.from_symplectic(z, x, phase)
[documentos] def argsort(self, weight=False, phase=False):
"""Return indices for sorting the rows of the table.
The default sort method is lexicographic sorting by qubit number.
By using the `weight` kwarg the output can additionally be sorted
by the number of non-identity terms in the Pauli, where the set of
all Paulis of a given weight are still ordered lexicographically.
Args:
weight (bool): Optionally sort by weight if ``True`` (Default: ``False``).
phase (bool): Optionally sort by phase before weight or order
(Default: ``False``).
Returns:
array: the indices for sorting the table.
"""
# Get order of each Pauli using
# I => 0, X => 1, Y => 2, Z => 3
x = self.x
z = self.z
order = 1 * (x & ~z) + 2 * (x & z) + 3 * (~x & z)
phases = self.phase
# Optionally get the weight of Pauli
# This is the number of non identity terms
if weight:
weights = np.sum(x | z, axis=1)
# To preserve ordering between successive sorts we
# are use the 'stable' sort method
indices = np.arange(self._num_paulis)
# Initial sort by phases
sort_inds = phases.argsort(kind="stable")
indices = indices[sort_inds]
order = order[sort_inds]
if phase:
phases = phases[sort_inds]
if weight:
weights = weights[sort_inds]
# Sort by order
for i in range(self.num_qubits):
sort_inds = order[:, i].argsort(kind="stable")
order = order[sort_inds]
indices = indices[sort_inds]
if weight:
weights = weights[sort_inds]
if phase:
phases = phases[sort_inds]
# If using weights we implement a sort by total number
# of non-identity Paulis
if weight:
sort_inds = weights.argsort(kind="stable")
indices = indices[sort_inds]
phases = phases[sort_inds]
# If sorting by phase we perform a final sort by the phase value
# of each pauli
if phase:
indices = indices[phases.argsort(kind="stable")]
return indices
[documentos] def sort(self, weight=False, phase=False):
"""Sort the rows of the table.
The default sort method is lexicographic sorting by qubit number.
By using the `weight` kwarg the output can additionally be sorted
by the number of non-identity terms in the Pauli, where the set of
all Paulis of a given weight are still ordered lexicographically.
**Example**
Consider sorting all a random ordering of all 2-qubit Paulis
.. code-block::
from numpy.random import shuffle
from qiskit.quantum_info.operators import PauliList
# 2-qubit labels
labels = ['II', 'IX', 'IY', 'IZ', 'XI', 'XX', 'XY', 'XZ',
'YI', 'YX', 'YY', 'YZ', 'ZI', 'ZX', 'ZY', 'ZZ']
# Shuffle Labels
shuffle(labels)
pt = PauliList(labels)
print('Initial Ordering')
print(pt)
# Lexicographic Ordering
srt = pt.sort()
print('Lexicographically sorted')
print(srt)
# Weight Ordering
srt = pt.sort(weight=True)
print('Weight sorted')
print(srt)
.. parsed-literal::
Initial Ordering
['YX', 'ZZ', 'XZ', 'YI', 'YZ', 'II', 'XX', 'XI', 'XY', 'YY', 'IX', 'IZ',
'ZY', 'ZI', 'ZX', 'IY']
Lexicographically sorted
['II', 'IX', 'IY', 'IZ', 'XI', 'XX', 'XY', 'XZ', 'YI', 'YX', 'YY', 'YZ',
'ZI', 'ZX', 'ZY', 'ZZ']
Weight sorted
['II', 'IX', 'IY', 'IZ', 'XI', 'YI', 'ZI', 'XX', 'XY', 'XZ', 'YX', 'YY',
'YZ', 'ZX', 'ZY', 'ZZ']
Args:
weight (bool): optionally sort by weight if ``True`` (Default: ``False``).
phase (bool): Optionally sort by phase before weight or order
(Default: ``False``).
Returns:
PauliList: a sorted copy of the original table.
"""
return self[self.argsort(weight=weight, phase=phase)]
[documentos] def unique(self, return_index=False, return_counts=False):
"""Return unique Paulis from the table.
**Example**
.. code-block::
from qiskit.quantum_info.operators import PauliList
pt = PauliList(['X', 'Y', '-X', 'I', 'I', 'Z', 'X', 'iZ'])
unique = pt.unique()
print(unique)
.. parsed-literal::
['X', 'Y', '-X', 'I', 'Z', 'iZ']
Args:
return_index (bool): If ``True``, also return the indices that
result in the unique array.
(Default: ``False``)
return_counts (bool): If ``True``, also return the number of times
each unique item appears in the table.
Returns:
PauliList: unique
the table of the unique rows.
unique_indices: np.ndarray, optional
The indices of the first occurrences of the unique values in
the original array. Only provided if ``return_index`` is ``True``.
unique_counts: np.array, optional
The number of times each of the unique values comes up in the
original array. Only provided if ``return_counts`` is ``True``.
"""
# Check if we need to stack the phase array
if np.any(self._phase != self._phase[0]):
# Create a single array of Pauli's and phases for calling np.unique on
# so that we treat different phased Pauli's as unique
array = np.hstack([self._z, self._x, self.phase.reshape((self.phase.shape[0], 1))])
else:
# All Pauli's have the same phase so we only need to sort the array
array = np.hstack([self._z, self._x])
# Get indexes of unique entries
if return_counts:
_, index, counts = np.unique(array, return_index=True, return_counts=True, axis=0)
else:
_, index = np.unique(array, return_index=True, axis=0)
# Sort the index so we return unique rows in the original array order
sort_inds = index.argsort()
index = index[sort_inds]
unique = PauliList(BasePauli(self._z[index], self._x[index], self._phase[index]))
# Concatinate return tuples
ret = (unique,)
if return_index:
ret += (index,)
if return_counts:
ret += (counts[sort_inds],)
if len(ret) == 1:
return ret[0]
return ret
# ---------------------------------------------------------------------
# BaseOperator methods
# ---------------------------------------------------------------------
[documentos] def tensor(self, other):
"""Return the tensor product with each Pauli in the list.
Args:
other (PauliList): another PauliList.
Returns:
PauliList: the list of tensor product Paulis.
Raises:
QiskitError: if other cannot be converted to a PauliList, does
not have either 1 or the same number of Paulis as
the current list.
"""
if not isinstance(other, PauliList):
other = PauliList(other)
return PauliList(super().tensor(other))
[documentos] def expand(self, other):
"""Return the expand product of each Pauli in the list.
Args:
other (PauliList): another PauliList.
Returns:
PauliList: the list of tensor product Paulis.
Raises:
QiskitError: if other cannot be converted to a PauliList, does
not have either 1 or the same number of Paulis as
the current list.
"""
if not isinstance(other, PauliList):
other = PauliList(other)
if len(other) not in [1, len(self)]:
raise QiskitError(
"Incompatible PauliLists. Other list must "
"have either 1 or the same number of Paulis."
)
return PauliList(super().expand(other))
[documentos] def compose(self, other, qargs=None, front=False, inplace=False):
"""Return the composition self∘other for each Pauli in the list.
Args:
other (PauliList): another PauliList.
qargs (None or list): qubits to apply dot product on (Default: ``None``).
front (bool): If True use `dot` composition method [default: ``False``].
inplace (bool): If ``True`` update in-place (default: ``False``).
Returns:
PauliList: the list of composed Paulis.
Raises:
QiskitError: if other cannot be converted to a PauliList, does
not have either 1 or the same number of Paulis as
the current list, or has the wrong number of qubits
for the specified ``qargs``.
"""
if qargs is None:
qargs = getattr(other, "qargs", None)
if not isinstance(other, PauliList):
other = PauliList(other)
if len(other) not in [1, len(self)]:
raise QiskitError(
"Incompatible PauliLists. Other list must "
"have either 1 or the same number of Paulis."
)
return PauliList(super().compose(other, qargs=qargs, front=front, inplace=inplace))
[documentos] def dot(self, other, qargs=None, inplace=False):
"""Return the composition other∘self for each Pauli in the list.
Args:
other (PauliList): another PauliList.
qargs (None or list): qubits to apply dot product on (Default: ``None``).
inplace (bool): If True update in-place (default: ``False``).
Returns:
PauliList: the list of composed Paulis.
Raises:
QiskitError: if other cannot be converted to a PauliList, does
not have either 1 or the same number of Paulis as
the current list, or has the wrong number of qubits
for the specified ``qargs``.
"""
return self.compose(other, qargs=qargs, front=True, inplace=inplace)
def _add(self, other, qargs=None):
"""Append two PauliLists.
If ``qargs`` are specified the other operator will be added
assuming it is identity on all other subsystems.
Args:
other (PauliList): another table.
qargs (None or list): optional subsystems to add on
(Default: ``None``)
Returns:
PauliList: the concatenated list ``self`` + ``other``.
"""
if qargs is None:
qargs = getattr(other, "qargs", None)
if not isinstance(other, PauliList):
other = PauliList(other)
self._op_shape._validate_add(other._op_shape, qargs)
base_phase = np.hstack((self._phase, other._phase))
if qargs is None or (sorted(qargs) == qargs and len(qargs) == self.num_qubits):
base_z = np.vstack([self._z, other._z])
base_x = np.vstack([self._x, other._x])
else:
# Pad other with identity and then add
padded = BasePauli(
np.zeros((other.size, self.num_qubits), dtype=bool),
np.zeros((other.size, self.num_qubits), dtype=bool),
np.zeros(other.size, dtype=int),
)
padded = padded.compose(other, qargs=qargs, inplace=True)
base_z = np.vstack([self._z, padded._z])
base_x = np.vstack([self._x, padded._x])
return PauliList(BasePauli(base_z, base_x, base_phase))
def _multiply(self, other):
"""Multiply each Pauli in the list by a phase.
Args:
other (complex or array): a complex number in [1, -1j, -1, 1j]
Returns:
PauliList: the list of Paulis other * self.
Raises:
QiskitError: if the phase is not in the set [1, -1j, -1, 1j].
"""
return PauliList(super()._multiply(other))
[documentos] def conjugate(self):
"""Return the conjugate of each Pauli in the list."""
return PauliList(super().conjugate())
[documentos] def transpose(self):
"""Return the transpose of each Pauli in the list."""
return PauliList(super().transpose())
[documentos] def adjoint(self):
"""Return the adjoint of each Pauli in the list."""
return PauliList(super().adjoint())
[documentos] def inverse(self):
"""Return the inverse of each Pauli in the list."""
return PauliList(super().adjoint())
# ---------------------------------------------------------------------
# Utility methods
# ---------------------------------------------------------------------
[documentos] def commutes(self, other, qargs=None):
"""Return True for each Pauli that commutes with other.
Args:
other (PauliList): another PauliList operator.
qargs (list): qubits to apply dot product on (default: ``None``).
Returns:
bool: ``True`` if Paulis commute, ``False`` if they anti-commute.
"""
if qargs is None:
qargs = getattr(other, "qargs", None)
if not isinstance(other, BasePauli):
other = PauliList(other)
return super().commutes(other, qargs=qargs)
[documentos] def anticommutes(self, other, qargs=None):
"""Return ``True`` if other Pauli that anticommutes with other.
Args:
other (PauliList): another PauliList operator.
qargs (list): qubits to apply dot product on (default: ``None``).
Returns:
bool: ``True`` if Paulis anticommute, ``False`` if they commute.
"""
return np.logical_not(self.commutes(other, qargs=qargs))
[documentos] def commutes_with_all(self, other):
"""Return indexes of rows that commute ``other``.
If ``other`` is a multi-row Pauli list the returned vector indexes rows
of the current PauliList that commute with *all* Paulis in other.
If no rows satisfy the condition the returned array will be empty.
Args:
other (PauliList): a single Pauli or multi-row PauliList.
Returns:
array: index array of the commuting rows.
"""
return self._commutes_with_all(other)
[documentos] def anticommutes_with_all(self, other):
"""Return indexes of rows that commute other.
If ``other`` is a multi-row Pauli list the returned vector indexes rows
of the current PauliList that anti-commute with *all* Paulis in other.
If no rows satisfy the condition the returned array will be empty.
Args:
other (PauliList): a single Pauli or multi-row PauliList.
Returns:
array: index array of the anti-commuting rows.
"""
return self._commutes_with_all(other, anti=True)
def _commutes_with_all(self, other, anti=False):
"""Return row indexes that commute with all rows in another PauliList.
Args:
other (PauliList): a PauliList.
anti (bool): if ``True`` return rows that anti-commute, otherwise
return rows that commute (Default: ``False``).
Returns:
array: index array of commuting or anti-commuting row.
"""
if not isinstance(other, PauliList):
other = PauliList(other)
comms = self.commutes(other[0])
(inds,) = np.where(comms == int(not anti))
for pauli in other[1:]:
comms = self[inds].commutes(pauli)
(new_inds,) = np.where(comms == int(not anti))
if new_inds.size == 0:
# No commuting rows
return new_inds
inds = inds[new_inds]
return inds
[documentos] def evolve(self, other, qargs=None, frame="h"):
r"""Evolve the Pauli by a Clifford.
This returns the Pauli :math:`P^\prime = C.P.C^\dagger`.
By choosing the parameter frame='s', this function returns the Schrödinger evolution of the Pauli
:math:`P^\prime = C.P.C^\dagger`. This option yields a faster calculation.
Args:
other (Pauli or Clifford or QuantumCircuit): The Clifford operator to evolve by.
qargs (list): a list of qubits to apply the Clifford to.
frame (string): 'h' for Heisenberg or 's' for Schrödinger framework.
Returns:
Pauli: the Pauli :math:`C.P.C^\dagger`.
Raises:
QiskitError: if the Clifford number of qubits and qargs don't match.
"""
from qiskit.circuit import Instruction, QuantumCircuit
from qiskit.quantum_info.operators.symplectic.clifford import Clifford
if qargs is None:
qargs = getattr(other, "qargs", None)
if not isinstance(other, (BasePauli, Instruction, QuantumCircuit, Clifford)):
# Convert to a PauliList
other = PauliList(other)
return PauliList(super().evolve(other, qargs=qargs, frame=frame))
[documentos] def to_labels(self, array=False):
r"""Convert a PauliList to a list Pauli string labels.
For large PauliLists converting using the ``array=True``
kwarg will be more efficient since it allocates memory for
the full Numpy array of labels in advance.
.. list-table:: Pauli Representations
:header-rows: 1
* - Label
- Symplectic
- Matrix
* - ``"I"``
- :math:`[0, 0]`
- :math:`\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}`
* - ``"X"``
- :math:`[1, 0]`
- :math:`\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}`
* - ``"Y"``
- :math:`[1, 1]`
- :math:`\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}`
* - ``"Z"``
- :math:`[0, 1]`
- :math:`\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}`
Args:
array (bool): return a Numpy array if ``True``, otherwise
return a list (Default: ``False``).
Returns:
list or array: The rows of the PauliList in label form.
"""
if (self.phase == 1).any():
prefix_len = 2
elif (self.phase > 0).any():
prefix_len = 1
else:
prefix_len = 0
str_len = self.num_qubits + prefix_len
ret = np.zeros(self.size, dtype=f"<U{str_len}")
iterator = self.label_iter()
for i in range(self.size):
ret[i] = next(iterator)
if array:
return ret
return ret.tolist()
[documentos] def to_matrix(self, sparse=False, array=False):
r"""Convert to a list or array of Pauli matrices.
For large PauliLists converting using the ``array=True``
kwarg will be more efficient since it allocates memory a full
rank-3 Numpy array of matrices in advance.
.. list-table:: Pauli Representations
:header-rows: 1
* - Label
- Symplectic
- Matrix
* - ``"I"``
- :math:`[0, 0]`
- :math:`\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}`
* - ``"X"``
- :math:`[1, 0]`
- :math:`\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}`
* - ``"Y"``
- :math:`[1, 1]`
- :math:`\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}`
* - ``"Z"``
- :math:`[0, 1]`
- :math:`\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}`
Args:
sparse (bool): if ``True`` return sparse CSR matrices, otherwise
return dense Numpy arrays (Default: ``False``).
array (bool): return as rank-3 numpy array if ``True``, otherwise
return a list of Numpy arrays (Default: ``False``).
Returns:
list: A list of dense Pauli matrices if ``array=False` and ``sparse=False`.
list: A list of sparse Pauli matrices if ``array=False`` and ``sparse=True``.
array: A dense rank-3 array of Pauli matrices if ``array=True``.
"""
if not array:
# We return a list of Numpy array matrices
return list(self.matrix_iter(sparse=sparse))
# For efficiency we also allow returning a single rank-3
# array where first index is the Pauli row, and second two
# indices are the matrix indices
dim = 2**self.num_qubits
ret = np.zeros((self.size, dim, dim), dtype=complex)
iterator = self.matrix_iter(sparse=sparse)
for i in range(self.size):
ret[i] = next(iterator)
return ret
# ---------------------------------------------------------------------
# Custom Iterators
# ---------------------------------------------------------------------
[documentos] def label_iter(self):
"""Return a label representation iterator.
This is a lazy iterator that converts each row into the string
label only as it is used. To convert the entire table to labels use
the :meth:`to_labels` method.
Returns:
LabelIterator: label iterator object for the PauliList.
"""
class LabelIterator(CustomIterator):
"""Label representation iteration and item access."""
def __repr__(self):
return f"<PauliList_label_iterator at {hex(id(self))}>"
def __getitem__(self, key):
return self.obj._to_label(self.obj._z[key], self.obj._x[key], self.obj._phase[key])
return LabelIterator(self)
[documentos] def matrix_iter(self, sparse=False):
"""Return a matrix representation iterator.
This is a lazy iterator that converts each row into the Pauli matrix
representation only as it is used. To convert the entire table to
matrices use the :meth:`to_matrix` method.
Args:
sparse (bool): optionally return sparse CSR matrices if ``True``,
otherwise return Numpy array matrices
(Default: ``False``)
Returns:
MatrixIterator: matrix iterator object for the PauliList.
"""
class MatrixIterator(CustomIterator):
"""Matrix representation iteration and item access."""
def __repr__(self):
return f"<PauliList_matrix_iterator at {hex(id(self))}>"
def __getitem__(self, key):
return self.obj._to_matrix(
self.obj._z[key], self.obj._x[key], self.obj._phase[key], sparse=sparse
)
return MatrixIterator(self)
# ---------------------------------------------------------------------
# Class methods
# ---------------------------------------------------------------------
[documentos] @classmethod
def from_symplectic(cls, z, x, phase=0):
"""Construct a PauliList from a symplectic data.
Args:
z (np.ndarray): 2D boolean Numpy array.
x (np.ndarray): 2D boolean Numpy array.
phase (np.ndarray or None): Optional, 1D integer array from Z_4.
Returns:
PauliList: the constructed PauliList.
"""
base_z, base_x, base_phase = cls._from_array(z, x, phase)
return cls(BasePauli(base_z, base_x, base_phase))
def _noncommutation_graph(self, qubit_wise):
"""Create an edge list representing the non-commutation graph (Pauli Graph).
An edge (i, j) is present if i and j are not commutable.
Args:
qubit_wise (bool): whether the commutation rule is applied to the whole operator,
or on a per-qubit basis.
Returns:
List[Tuple(int,int)]: A list of pairs of indices of the PauliList that are not commutable.
"""
# convert a Pauli operator into int vector where {I: 0, X: 2, Y: 3, Z: 1}
mat1 = np.array(
[op.z + 2 * op.x for op in self],
dtype=np.int8,
)
mat2 = mat1[:, None]
# This is 0 (false-y) iff one of the operators is the identity and/or both operators are the
# same. In other cases, it is non-zero (truth-y).
qubit_anticommutation_mat = (mat1 * mat2) * (mat1 - mat2)
# 'adjacency_mat[i, j]' is True iff Paulis 'i' and 'j' do not commute in the given strategy.
if qubit_wise:
adjacency_mat = np.logical_or.reduce(qubit_anticommutation_mat, axis=2)
else:
# Don't commute if there's an odd number of element-wise anti-commutations.
adjacency_mat = np.logical_xor.reduce(qubit_anticommutation_mat, axis=2)
# Convert into list where tuple elements are non-commuting operators. We only want to
# results from one triangle to avoid symmetric duplications.
return list(zip(*np.where(np.triu(adjacency_mat, k=1))))
def _create_graph(self, qubit_wise):
"""Transform measurement operator grouping problem into graph coloring problem
Args:
qubit_wise (bool): whether the commutation rule is applied to the whole operator,
or on a per-qubit basis.
Returns:
rustworkx.PyGraph: A class of undirected graphs
"""
edges = self._noncommutation_graph(qubit_wise)
graph = rx.PyGraph()
graph.add_nodes_from(range(self.size))
graph.add_edges_from_no_data(edges)
return graph
[documentos] def group_qubit_wise_commuting(self):
"""Partition a PauliList into sets of mutually qubit-wise commuting Pauli strings.
Returns:
List[PauliList]: List of PauliLists where each PauliList contains commutable Pauli operators.
"""
return self.group_commuting(qubit_wise=True)
[documentos] def group_commuting(self, qubit_wise=False):
"""Partition a PauliList into sets of commuting Pauli strings.
Args:
qubit_wise (bool): whether the commutation rule is applied to the whole operator,
or on a per-qubit basis. For example:
.. code-block:: python
>>> from qiskit.quantum_info import PauliList
>>> op = PauliList(["XX", "YY", "IZ", "ZZ"])
>>> op.group_commuting()
[PauliList(['XX', 'YY']), PauliList(['IZ', 'ZZ'])]
>>> op.group_commuting(qubit_wise=True)
[PauliList(['XX']), PauliList(['YY']), PauliList(['IZ', 'ZZ'])]
Returns:
List[PauliList]: List of PauliLists where each PauliList contains commuting Pauli operators.
"""
graph = self._create_graph(qubit_wise)
# Keys in coloring_dict are nodes, values are colors
coloring_dict = rx.graph_greedy_color(graph)
groups = defaultdict(list)
for idx, color in coloring_dict.items():
groups[color].append(idx)
return [self[group] for group in groups.values()]