English
Languages
English
Japanese
German
Korean
Shortcuts

Source code for qiskit.quantum_info.operators.symplectic.stabilizer_table

# 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.
"""
Symplectic Stabilizer Table Class
"""
# pylint: disable=invalid-name, abstract-method

import numpy as np

from qiskit.exceptions import QiskitError
from qiskit.quantum_info.operators.custom_iterator import CustomIterator
from qiskit.quantum_info.operators.symplectic.pauli_table import PauliTable


[docs]class StabilizerTable(PauliTable): r"""Symplectic representation of a list Stabilizer matrices. **Symplectic Representation** The symplectic representation of a single-qubit Stabilizer matrix is a pair of boolean values :math:`[x, z]` and a boolean phase `p` such that the Stabilizer matrix is given by :math:`S = (-1)^p \sigma_z^z.\sigma_x^x`. The correspondence between labels, symplectic representation, stabilizer matrices, and Pauli matrices for the single-qubit case is shown in the following table. .. list-table:: Table 1: Stabilizer Representations :header-rows: 1 * - Label - Phase - Symplectic - Matrix - Pauli * - ``"+I"`` - 0 - :math:`[0, 0]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`I` * - ``"-I"`` - 1 - :math:`[0, 0]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`-I` * - ``"X"`` - 0 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}` - :math:`X` * - ``"-X"`` - 1 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}` - :math:`-X` * - ``"Y"`` - 0 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}` - :math:`iY` * - ``"-Y"`` - 1 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}` - :math:`-iY` * - ``"Z"`` - 0 - :math:`[0, 1]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`Z` * - ``"-Z"`` - 1 - :math:`[0, 1]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`-Z` Internally this is stored as a length `N` boolean phase vector :math:`[p_{N-1}, ..., p_{0}]` and a :class:`PauliTable` :math:`M \times 2N` boolean matrix: .. math:: \left(\begin{array}{ccc|ccc} x_{0,0} & ... & x_{0,N-1} & z_{0,0} & ... & z_{0,N-1} \\ x_{1,0} & ... & x_{1,N-1} & z_{1,0} & ... & z_{1,N-1} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ x_{M-1,0} & ... & x_{M-1,N-1} & z_{M-1,0} & ... & z_{M-1,N-1} \end{array}\right) where each row is a block vector :math:`[X_i, Z_i]` with :math:`X_i = [x_{i,0}, ..., x_{i,N-1}]`, :math:`Z_i = [z_{i,0}, ..., z_{i,N-1}]` is the symplectic representation of an `N`-qubit Pauli. This representation is based on reference [1]. StabilizerTable's can be created from a list of labels using :meth:`from_labels`, and converted to a list of labels or a list of matrices using :meth:`to_labels` and :meth:`to_matrix` respectively. **Group Product** The product of the stabilizer elements is defined with respect to the matrix multiplication of the matrices in Table 1. In terms of stabilizes labels the dot product group structure is +-------+----+----+----+----+ | A.B | I | X | Y | Z | +=======+====+====+====+====+ | **I** | I | X | Y | Z | +-------+----+----+----+----+ | **X** | X | I | -Z | Y | +-------+----+----+----+----+ | **Y** | Y | Z | -I | -X | +-------+----+----+----+----+ | **Z** | Z | -Y | X | I | +-------+----+----+----+----+ The :meth:`dot` method will return the output for :code:`row.dot(col) = row.col`, while the :meth:`compose` will return :code:`row.compose(col) = col.row` from the above table. Note that while this dot product is different to the matrix product of the :class:`PauliTable`, it does not change the commutation structure of elements. Hence :meth:`commutes:` will be the same for the same labels. **Qubit Ordering** The qubits are ordered in the table such the least significant qubit `[x_{i, 0}, z_{i, 0}]` is the first element of each of the :math:`X_i, Z_i` vector blocks. This is the opposite order to position in string labels or matrix tensor products where the least significant qubit is the right-most string character. For example Pauli ``"ZX"`` has ``"X"`` on qubit-0 and ``"Z"`` on qubit 1, and would have symplectic vectors :math:`x=[1, 0]`, :math:`z=[0, 1]`. **Data Access** Subsets of rows can be accessed using the list access ``[]`` operator and will return a table view of part of the StabilizerTable. The underlying phase vector and Pauli array can be directly accessed using the :attr:`phase` and :attr:`array` properties respectively. The sub-arrays for only the `X` or `Z` blocks can be accessed using the :attr:`X` and :attr:`Z` properties respectively. The Pauli part of the Stabilizer table can be viewed and accessed as a :class:`PauliTable` object using the :attr:`pauli` property. Note that this doesn't copy the underlying array so any changes made to the Pauli table will also change the stabilizer table. **Iteration** Rows in the Stabilizer 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. References: 1. S. Aaronson, D. Gottesman, *Improved Simulation of Stabilizer Circuits*, Phys. Rev. A 70, 052328 (2004). `arXiv:quant-ph/0406196 <https://arxiv.org/abs/quant-ph/0406196>`_ """
[docs] def __init__(self, data, phase=None): """Initialize the StabilizerTable. Args: data (array or str or PauliTable): input PauliTable data. phase (array or bool or None): optional phase vector for input data (Default: None). Raises: QiskitError: if input array or phase vector has an invalid shape. Additional Information: The input array is not copied so multiple Pauli and Stabilizer tables can share the same underlying array. """ if isinstance(data, str) and phase is None: pauli, phase = StabilizerTable._from_label(data) elif isinstance(data, StabilizerTable): pauli = data._array if phase is None: phase = data._phase else: pauli = data # Initialize the Pauli table super().__init__(pauli) # Initialize the phase vector if phase is None or phase is False: self._phase = np.zeros(self.size, dtype=bool) elif phase is True: self._phase = np.ones(self.size, dtype=bool) else: self._phase = np.asarray(phase, dtype=bool) if self._phase.shape != (self.size, ): raise QiskitError("Phase vector is incorrect shape.")
def __repr__(self): return 'StabilizerTable(\n{},\nphase={})'.format( repr(self._array), repr(self._phase)) def __str__(self): """String representation""" return 'StabilizerTable: {}'.format(self.to_labels()) def __eq__(self, other): """Test if two StabilizerTables are equal""" if isinstance(other, StabilizerTable): return np.all(self._phase == other._phase) and self.pauli == other.pauli return False
[docs] def copy(self): """Return a copy of the StabilizerTable.""" return StabilizerTable(self._array.copy(), self._phase.copy())
# --------------------------------------------------------------------- # PauliTable and phase access # --------------------------------------------------------------------- @property def pauli(self): """Return PauliTable""" return PauliTable(self._array) @pauli.setter def pauli(self, value): if not isinstance(value, PauliTable): value = PauliTable(value) self._array[:, :] = value._array @property def phase(self): """Return phase vector""" return self._phase @phase.setter def phase(self, value): self._phase[:] = value # --------------------------------------------------------------------- # Array methods # --------------------------------------------------------------------- def __getitem__(self, key): """Return a view of StabilizerTable""" if isinstance(key, int): key = [key] return StabilizerTable(self._array[key], self._phase[key]) def __setitem__(self, key, value): """Update StabilizerTable""" if not isinstance(value, StabilizerTable): value = StabilizerTable(value) self._array[key] = value.array self._phase[key] = value.phase
[docs] def delete(self, ind, qubit=False): """Return a copy with Stabilizer rows deleted from table. When deleting qubit columns, qubit-0 is the right-most (largest index) column, and qubit-(N-1) is the left-most (0 index) column 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 Stabilizer rows (Default: False). Returns: StabilizerTable: the resulting table with the entries removed. Raises: QiskitError: if ind is out of bounds for the array size or number of qubits. """ if qubit: # When deleting qubit columns we don't need to modify # the phase vector table = super().delete(ind, True) return StabilizerTable(table, self._phase) if isinstance(ind, int): ind = [ind] if max(ind) >= self.size: raise QiskitError("Indices {} are not all less than the size" " of the SatbilizerTable ({})".format(ind, self.size)) return StabilizerTable(np.delete(self._array, ind, axis=0), np.delete(self._phase, ind, axis=0))
[docs] def insert(self, ind, value, qubit=False): """Insert stabilizers's into the table. When inserting qubit columns, qubit-0 is the right-most (largest index) column, and qubit-(N-1) is the left-most (0 index) column of the underlying :attr:`X` and :attr:`Z` arrays. Args: ind (int): index to insert at. value (StabilizerTable): values to insert. qubit (bool): if True delete qubit columns, otherwise delete Pauli rows (Default: False). Returns: StabilizerTable: 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, StabilizerTable): value = StabilizerTable(value) # Update PauliTable component table = super().insert(ind, value, qubit=qubit) # Update phase vector if not qubit: phase = np.insert(self._phase, ind, value._phase, axis=0) else: phase = np.logical_xor(self._phase, value._phase) return StabilizerTable(table, phase)
[docs] def argsort(self, weight=False): """Return indices for sorting the rows of the PauliTable. The default sort method is lexicographic sorting of Paulis by qubit number. By using the `weight` kwarg the output can additionally be sorted by the number of non-identity terms in the Stabilizer, where the set of all Pauli's of a given weight are still ordered lexicographically. This does not sort based on phase values. It will preserve the original order of rows with the same Pauli's but different phases. Args: weight (bool): optionally sort by weight if True (Default: False). Returns: array: the indices for sorting the table. """ return super().argsort(weight=weight)
[docs] def sort(self, weight=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 Pauli's of a given weight are still ordered lexicographically. This does not sort based on phase values. It will preserve the original order of rows with the same Pauli's but different phases. Consider sorting all a random ordering of all 2-qubit Paulis .. jupyter-execute:: from numpy.random import shuffle from qiskit.quantum_info.operators import StabilizerTable # 2-qubit labels labels = ['+II', '+IX', '+IY', '+IZ', '+XI', '+XX', '+XY', '+XZ', '+YI', '+YX', '+YY', '+YZ', '+ZI', '+ZX', '+ZY', '+ZZ', '-II', '-IX', '-IY', '-IZ', '-XI', '-XX', '-XY', '-XZ', '-YI', '-YX', '-YY', '-YZ', '-ZI', '-ZX', '-ZY', '-ZZ'] # Shuffle Labels shuffle(labels) st = StabilizerTable.from_labels(labels) print('Initial Ordering') print(st) # Lexicographic Ordering srt = st.sort() print('Lexicographically sorted') print(srt) # Weight Ordering srt = st.sort(weight=True) print('Weight sorted') print(srt) Args: weight (bool): optionally sort by weight if True (Default: False). Returns: StabilizerTable: a sorted copy of the original table. """ return super().sort(weight=weight)
[docs] def unique(self, return_index=False, return_counts=False): """Return unique stabilizers from the table. **Example** .. jupyter-execute:: from qiskit.quantum_info.operators import StabilizerTable st = StabilizerTable.from_labels(['+X', '+I', '-I', '-X', '+X', '-X', '+I']) unique = st.unique() print(unique) 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: StabilizerTable: 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. """ # Combine array and phases into single array for sorting stack = np.hstack([self._array, self._phase.reshape((self.size, 1))]) if return_counts: _, index, counts = np.unique(stack, return_index=True, return_counts=True, axis=0) else: _, index = np.unique(stack, 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 = self[index] # Concatenate 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
# --------------------------------------------------------------------- # Utility methods # ---------------------------------------------------------------------
[docs] def tensor(self, other): """Return the tensor output product of two tables. This returns the combination of the tensor product of all stabilizers in the `current` table with all stabilizers in the `other` table. The `other` tables qubits will be the least-significant in the returned table. This is the opposite tensor order to :meth:`tensor`. **Example** .. jupyter-execute:: from qiskit.quantum_info.operators import StabilizerTable current = StabilizerTable.from_labels(['+I', '-X']) other = StabilizerTable.from_labels(['-Y', '+Z']) print(current.tensor(other)) Args: other (StabilizerTable): another StabilizerTable. Returns: StabilizerTable: the tensor outer product table. Raises: QiskitError: if other cannot be converted to a StabilizerTable. """ if not isinstance(other, StabilizerTable): other = StabilizerTable(other) pauli = super().tensor(other) phase1, phase2 = self._block_stack(self.phase, other.phase) phase = np.logical_xor(phase1, phase2) return StabilizerTable(pauli, phase)
[docs] def expand(self, other): """Return the expand output product of two tables. This returns the combination of the tensor product of all stabilizers in the `other` table with all stabilizers in the `current` table. The `current` tables qubits will be the least-significant in the returned table. This is the opposite tensor order to :meth:`tensor`. **Example** .. jupyter-execute:: from qiskit.quantum_info.operators import StabilizerTable current = StabilizerTable.from_labels(['+I', '-X']) other = StabilizerTable.from_labels(['-Y', '+Z']) print(current.expand(other)) Args: other (StabilizerTable): another StabilizerTable. Returns: StabilizerTable: the expand outer product table. Raises: QiskitError: if other cannot be converted to a StabilizerTable. """ if not isinstance(other, StabilizerTable): other = StabilizerTable(other) pauli = super().expand(other) phase1, phase2 = self._block_stack(self.phase, other.phase) phase = np.logical_xor(phase1, phase2) return StabilizerTable(pauli, phase)
[docs] def compose(self, other, qargs=None, front=False): """Return the compose output product of two tables. This returns the combination of the compose product of all stabilizers in the current table with all stabilizers in the other table. The individual stabilizer compose product is given by +----------------------+----+----+----+----+ | :code:`A.compose(B)` | I | X | Y | Z | +======================+====+====+====+====+ | **I** | I | X | Y | Z | +----------------------+----+----+----+----+ | **X** | X | I | Z | -Y | +----------------------+----+----+----+----+ | **Y** | Y | -Z | -I | X | +----------------------+----+----+----+----+ | **Z** | Z | Y | -X | I | +----------------------+----+----+----+----+ If `front=True` the composition will be given by the :meth:`dot` method. **Example** .. jupyter-execute:: from qiskit.quantum_info.operators import StabilizerTable current = StabilizerTable.from_labels(['+I', '-X']) other = StabilizerTable.from_labels(['+X', '-Z']) print(current.compose(other)) Args: other (StabilizerTable): another StabilizerTable. qargs (None or list): qubits to apply compose product on (Default: None). front (bool): If True use `dot` composition method (default: False). Returns: StabilizerTable: the compose outer product table. Raises: QiskitError: if other cannot be converted to a StabilizerTable. """ if not isinstance(other, StabilizerTable): other = StabilizerTable(other) if qargs is None and other.num_qubits != self.num_qubits: raise QiskitError("other StabilizerTable must be on the same number of qubits.") if qargs and other.num_qubits != len(qargs): raise QiskitError("Number of qubits in the other StabilizerTable does not match qargs.") # Stack X and Z blocks for output size x1, x2 = self._block_stack(self.X, other.X) z1, z2 = self._block_stack(self.Z, other.Z) phase1, phase2 = self._block_stack(self.phase, other.phase) if qargs is not None: ret_x, ret_z = x1.copy(), z1.copy() x1 = x1[:, qargs] z1 = z1[:, qargs] ret_x[:, qargs] = x1 ^ x2 ret_z[:, qargs] = z1 ^ z2 pauli = np.hstack([ret_x, ret_z]) else: pauli = np.hstack((x1 ^ x2, z1 ^ z2)) # We pick up a minus sign for products: # Y.Y = -I, X.Y = -Z, Y.Z = -X, Z.X = -Y if front: minus = (x1 & z2 & (x2 | z1)) | (~x1 & x2 & z1 & ~z2) else: minus = (x2 & z1 & (x1 | z2)) | (~x2 & x1 & z2 & ~z1) phase_shift = np.array(np.sum(minus, axis=1) % 2, dtype=bool) phase = phase_shift ^ phase1 ^ phase2 return StabilizerTable(pauli, phase)
[docs] def dot(self, other, qargs=None): """Return the dot output product of two tables. This returns the combination of the compose product of all stabilizers in the current table with all stabilizers in the other table. The individual stabilizer dot product is given by +------------------+----+----+----+----+ | :code:`A.dot(B)` | I | X | Y | Z | +==================+====+====+====+====+ | **I** | I | X | Y | Z | +------------------+----+----+----+----+ | **X** | X | I | -Z | Y | +------------------+----+----+----+----+ | **Y** | Y | Z | -I | -X | +------------------+----+----+----+----+ | **Z** | Z | -Y | X | I | +------------------+----+----+----+----+ **Example** .. jupyter-execute:: from qiskit.quantum_info.operators import StabilizerTable current = StabilizerTable.from_labels(['+I', '-X']) other = StabilizerTable.from_labels(['+X', '-Z']) print(current.dot(other)) Args: other (StabilizerTable): another StabilizerTable. qargs (None or list): qubits to apply dot product on (Default: None). Returns: StabilizerTable: the dot outer product table. Raises: QiskitError: if other cannot be converted to a StabilizerTable. """ return super().dot(other, qargs=qargs)
def _add(self, other, qargs=None): """Append with another StabilizerTable. If ``qargs`` are specified the other operator will be added assuming it is identity on all other subsystems. Args: other (StabilizerTable): another table. qargs (None or list): optional subsystems to add on (Default: None) Returns: StabilizerTable: the concatinated table self + other. """ if qargs is None: qargs = getattr(other, 'qargs', None) if not isinstance(other, StabilizerTable): other = StabilizerTable(other) self._validate_add_dims(other, qargs) if qargs is None or (sorted(qargs) == qargs and len(qargs) == self.num_qubits): return StabilizerTable(np.vstack((self._array, other._array)), np.hstack((self._phase, other._phase))) # Pad other with identity and then add padded = StabilizerTable( np.zeros((1, 2 * self.num_qubits), dtype=bool)) padded = padded.compose(other, qargs=qargs) return StabilizerTable( np.vstack((self._array, padded._array)), np.hstack((self._phase, padded._phase))) def _multiply(self, other): """Multiply (XOR) phase vector of the StabilizerTable. This updates the phase vector of the table. Allowed values for multiplication are ``False``, ``True``, 1 or -1. Multiplying by -1 or ``False`` is equivalent. As is multiplying by 1 or ``True``. Args: other (bool or int): a Boolean value. Returns: StabilizerTable: the updated stabilizer table. Raises: QiskitError: if other is not in (False, True, 1, -1). """ # Numeric (integer) value case if not isinstance(other, bool) and other not in [1, -1]: raise QiskitError( "Can only multiply a Stabilizer value by +1 or -1 phase.") # We have to be careful we don't cast True <-> +1 when # we store -1 phase as boolen True value if (isinstance(other, bool) and other) or other == -1: ret = self.copy() ret._phase ^= True return ret return self # --------------------------------------------------------------------- # Representation conversions # ---------------------------------------------------------------------
[docs] @classmethod def from_labels(cls, labels): r"""Construct a StabilizerTable from a list of Pauli stabilizer strings. Pauli Stabilizer string labels are Pauli strings with an optional ``"+"`` or ``"-"`` character. If there is no +/-sign a + phase is used by default. .. list-table:: Stabilizer Representations :header-rows: 1 * - Label - Phase - Symplectic - Matrix - Pauli * - ``"+I"`` - 0 - :math:`[0, 0]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`I` * - ``"-I"`` - 1 - :math:`[0, 0]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`-I` * - ``"X"`` - 0 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}` - :math:`X` * - ``"-X"`` - 1 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}` - :math:`-X` * - ``"Y"`` - 0 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}` - :math:`iY` * - ``"-Y"`` - 1 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}` - :math:`-iY` * - ``"Z"`` - 0 - :math:`[0, 1]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`Z` * - ``"-Z"`` - 1 - :math:`[0, 1]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`-Z` Args: labels (list): Pauli stabilizer string label(es). Returns: StabilizerTable: the constructed StabilizerTable. Raises: QiskitError: If the input list is empty or contains invalid Pauli stabilizer strings. """ if isinstance(labels, str): labels = [labels] n_paulis = len(labels) if n_paulis == 0: raise QiskitError("Input Pauli list is empty.") # Get size from first Pauli pauli, phase = cls._from_label(labels[0]) table = np.zeros((n_paulis, len(pauli)), dtype=bool) phases = np.zeros(n_paulis, dtype=bool) table[0], phases[0] = pauli, phase for i in range(1, n_paulis): table[i], phases[i] = cls._from_label(labels[i]) return cls(table, phases)
[docs] def to_labels(self, array=False): r"""Convert a StabilizerTable to a list Pauli stabilizer string labels. For large StabilizerTables 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:: Stabilizer Representations :header-rows: 1 * - Label - Phase - Symplectic - Matrix - Pauli * - ``"+I"`` - 0 - :math:`[0, 0]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`I` * - ``"-I"`` - 1 - :math:`[0, 0]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`-I` * - ``"X"`` - 0 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}` - :math:`X` * - ``"-X"`` - 1 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}` - :math:`-X` * - ``"Y"`` - 0 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}` - :math:`iY` * - ``"-Y"`` - 1 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}` - :math:`-iY` * - ``"Z"`` - 0 - :math:`[0, 1]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`Z` * - ``"-Z"`` - 1 - :math:`[0, 1]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`-Z` Args: array (bool): return a Numpy array if True, otherwise return a list (Default: False). Returns: list or array: The rows of the StabilizerTable in label form. """ ret = np.zeros(self.size, dtype='<U{}'.format(1 + self._num_qubits)) for i in range(self.size): ret[i] = self._to_label(self._array[i], self._phase[i]) if array: return ret return ret.tolist()
[docs] def to_matrix(self, sparse=False, array=False): r"""Convert to a list or array of Stabilizer matrices. For large StabilizerTables converting using the ``array=True`` kwarg will be more efficient since it allocates memory for the full rank-3 Numpy array of matrices in advance. .. list-table:: Stabilizer Representations :header-rows: 1 * - Label - Phase - Symplectic - Matrix - Pauli * - ``"+I"`` - 0 - :math:`[0, 0]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`I` * - ``"-I"`` - 1 - :math:`[0, 0]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`-I` * - ``"X"`` - 0 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}` - :math:`X` * - ``"-X"`` - 1 - :math:`[1, 0]` - :math:`\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}` - :math:`-X` * - ``"Y"`` - 0 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}` - :math:`iY` * - ``"-Y"`` - 1 - :math:`[1, 1]` - :math:`\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}` - :math:`-iY` * - ``"Z"`` - 0 - :math:`[0, 1]` - :math:`\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}` - :math:`Z` * - ``"-Z"`` - 1 - :math:`[0, 1]` - :math:`\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}` - :math:`-Z` 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 [self._to_matrix(pauli, phase, sparse=sparse) for pauli, phase in zip(self._array, self._phase)] # 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=float) for i in range(self.size): ret[i] = self._to_matrix(self._array[i], self._phase[i]) return ret
@staticmethod def _from_label(label): """Return the symplectic representation of a Pauli stabilizer string""" # Check if first character is '+' or '-' phase = False if label[0] in ['-', '+']: phase = (label[0] == '-') label = label[1:] return PauliTable._from_label(label), phase @staticmethod def _to_label(pauli, phase): """Return the Pauli stabilizer string from symplectic representation.""" # pylint: disable=arguments-differ # Cast in symplectic representation # This should avoid a copy if the pauli is already a row # in the symplectic table label = PauliTable._to_label(pauli) if phase: return '-' + label return '+' + label @staticmethod def _to_matrix(pauli, phase, sparse=False): """"Return the Pauli stabilizer matrix from symplectic representation. Args: pauli (array): symplectic Pauli vector. phase (bool): the phase value for the Pauli. sparse (bool): if True return a sparse CSR matrix, otherwise return a dense Numpy array (Default: False). Returns: array: if sparse=False. csr_matrix: if sparse=True. """ # pylint: disable=arguments-differ mat = PauliTable._to_matrix(pauli, sparse=sparse, real_valued=True) if phase: mat *= -1 return mat # --------------------------------------------------------------------- # Custom Iterators # ---------------------------------------------------------------------
[docs] 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 StabilizerTable. """ class LabelIterator(CustomIterator): """Label representation iteration and item access.""" def __repr__(self): return "<StabilizerTable_label_iterator at {}>".format(hex(id(self))) def __getitem__(self, key): return self.obj._to_label(self.obj.array[key], self.obj.phase[key]) return LabelIterator(self)
[docs] 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 StabilizerTable. """ class MatrixIterator(CustomIterator): """Matrix representation iteration and item access.""" def __repr__(self): return "<StabilizerTable_matrix_iterator at {}>".format(hex(id(self))) def __getitem__(self, key): return self.obj._to_matrix(self.obj.array[key], self.obj.phase[key], sparse=sparse) return MatrixIterator(self)

© Copyright 2020, Qiskit Development Team. Last updated on 2021/02/18.

Built with Sphinx using a theme provided by Read the Docs.