---
title: PauliList (latest version)
description: API reference for qiskit.quantum_info.PauliList in the latest version of qiskit
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.quantum_info.PauliList
---

# PauliList

*class* `qiskit.quantum_info.PauliList(data)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L33-L1242)

Bases: `BasePauli`, `LinearMixin`, `GroupMixin`

List of N-qubit Pauli operators.

This class is an efficient representation of a list of [`Pauli`](/docs/api/qiskit/qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli") operators. It supports 1D numpy array indexing returning a [`Pauli`](/docs/api/qiskit/qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli") for integer indexes or a [`PauliList`](#qiskit.quantum_info.PauliList "qiskit.quantum_info.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 [`Pauli`](/docs/api/qiskit/qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli").
>
> **`PauliList(Pauli) and PauliList(list[Pauli])`**
>
> where Pauli is [`Pauli`](/docs/api/qiskit/qiskit.quantum_info.Pauli "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,

```python
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)
```

```text
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.

```python
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]))
```

```text
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 [`label_iter()`](#qiskit.quantum_info.PauliList.label_iter "qiskit.quantum_info.PauliList.label_iter") and [`matrix_iter()`](#qiskit.quantum_info.PauliList.matrix_iter "qiskit.quantum_info.PauliList.matrix_iter") methods.

Initialize the PauliList.

**Parameters**

**data** ([*Pauli*](/docs/api/qiskit/qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")  *or*[*list*](https://docs.python.org/3/library/stdtypes.html#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**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.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.

## Attributes

### dim

Return tuple (input\_shape, output\_shape).

### num\_qubits

Return the number of qubits if a N-qubit operator or None otherwise.

### phase

Return the phase exponent of the PauliList.

### qargs

Return the qargs for the operator.

### settings

Return settings.

### shape

The full shape of the `array()`

### size

The number of Pauli rows in the table.

### x

The x array for the symplectic representation.

### z

The z array for the symplectic representation.

## Methods

### adjoint

`adjoint()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L828-L830)

Return the adjoint of each Pauli in the list.

### anticommutes

`anticommutes(other, qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L856-L866)

Return `True` if the other Pauli anticommutes with this one.

**Parameters**

- **other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – another PauliList operator.
- **qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)) – qubits to apply dot product on (default: `None`).

**Returns**

`True` if Paulis anticommute, `False` if they commute.

**Return type**

[bool](https://docs.python.org/3/library/functions.html#bool)

### anticommutes\_with\_all

`anticommutes_with_all(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L883-L896)

Return indexes of rows that anticommute with the other Pauli list.

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.

**Parameters**

**other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – a single Pauli or multi-row PauliList.

**Returns**

index array of the anti-commuting rows.

**Return type**

[array](/docs/api/qiskit/qiskit.primitives.BitArray#array "qiskit.primitives.BitArray.array")

### argsort

`argsort(weight=False, phase=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L476-L537)

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.

**Parameters**

- **weight** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Optionally sort by weight if `True` (Default: `False`).
- **phase** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Optionally sort by phase before weight or order (Default: `False`).

**Returns**

the indices for sorting the table.

**Return type**

[array](/docs/api/qiskit/qiskit.primitives.BitArray#array "qiskit.primitives.BitArray.array")

### commutes

`commutes(other, qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L840-L854)

Return True for each Pauli that commutes with other.

**Parameters**

- **other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – another PauliList operator.
- **qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)) – qubits to apply dot product on (default: `None`).

**Returns**

`True` if Paulis commute, `False` if they anti-commute.

**Return type**

[bool](https://docs.python.org/3/library/functions.html#bool)

### commutes\_with\_all

`commutes_with_all(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L868-L881)

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.

**Parameters**

**other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – a single Pauli or multi-row PauliList.

**Returns**

index array of the commuting rows.

**Return type**

[array](/docs/api/qiskit/qiskit.primitives.BitArray#array "qiskit.primitives.BitArray.array")

### compose

`compose(other, qargs=None, front=False, inplace=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L712-L745)

Return the composition self∘other for each Pauli in the list.

**Parameters**

- **other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – another PauliList.
- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – qubits to apply dot product on (Default: `None`).
- **front** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True use dot composition method \[default: `False`].
- **inplace** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If `True` update in-place (default: `False`).

**Returns**

the list of composed Paulis.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.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`.

### conjugate

`conjugate()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L820-L822)

Return the conjugate of each Pauli in the list.

### copy

`copy()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/base_pauli.py#L64-L73)

Make a deep copy of current operator.

### delete

`delete(ind, qubit=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L365-L410)

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 `X` and `Z` arrays.

**Parameters**

- **ind** ([*int*](https://docs.python.org/3/library/functions.html#int)  *or*[*list*](https://docs.python.org/3/library/stdtypes.html#list)) – index(es) to delete.
- **qubit** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – if `True` delete qubit columns, otherwise delete Pauli rows (Default: `False`).

**Returns**

the resulting table with the entries removed.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if `ind` is out of bounds for the array size or number of qubits.

### dot

`dot(other, qargs=None, inplace=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L747-L764)

Return the composition other∘self for each Pauli in the list.

**Parameters**

- **other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – another PauliList.
- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – qubits to apply dot product on (Default: `None`).
- **inplace** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True update in-place (default: `False`).

**Returns**

the list of composed Paulis.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.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`.

### equiv

`equiv(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L241-L253)

Entrywise comparison of Pauli equivalence up to global phase.

**Parameters**

**other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")  *or*[*Pauli*](/docs/api/qiskit/qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")) – a comparison object.

**Returns**

**An array of `True` or `False` for entrywise equivalence**

of the current table.

**Return type**

np.ndarray

### evolve

`evolve(other, qargs=None, frame='h')`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L922-L959)

Performs either Heisenberg (default) or Schrödinger picture evolution of the Pauli by a Clifford and returns the evolved Pauli.

Schrödinger picture evolution can be chosen by passing parameter `frame='s'`. This option yields a faster calculation.

Heisenberg picture evolves the Pauli as $P^\prime = C^\dagger.P.C$.

Schrödinger picture evolves the Pauli as $P^\prime = C.P.C^\dagger$.

**Parameters**

- **other** ([*Pauli*](/docs/api/qiskit/qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")  *or*[*Clifford*](/docs/api/qiskit/qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")  *or*[*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The Clifford operator to evolve by.
- **qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)) – a list of qubits to apply the Clifford to.
- **frame** (*string*) – `'h'` for Heisenberg (default) or `'s'` for Schrödinger framework.

**Returns**

the Pauli $C^\dagger.P.C$ (Heisenberg picture) or the Pauli $C.P.C^\dagger$ (Schrödinger picture).

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the Clifford number of qubits and qargs don’t match.

### expand

`expand(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L689-L710)

Return the expand product of each Pauli in the list.

**Parameters**

**other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – another PauliList.

**Returns**

the list of tensor product Paulis.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if other cannot be converted to a PauliList, does not have either 1 or the same number of Paulis as the current list.

### from\_symplectic

*classmethod* `from_symplectic(z, x, phase=0)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1118-L1135)

Construct a PauliList from a symplectic data.

**Parameters**

- **z** (*np.ndarray*) – 2D boolean Numpy array.
- **x** (*np.ndarray*) – 2D boolean Numpy array.
- **phase** (*np.ndarray or None*) – 1D integer array from Z\_4.

**Returns**

the constructed PauliList.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

### group\_commuting

`group_commuting(qubit_wise=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1220-L1242)

Partition a PauliList into sets of commuting Pauli strings.

**Parameters**

**qubit\_wise** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) –

whether the commutation rule is applied to the whole operator, or on a per-qubit basis. For example:

```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 of PauliLists where each PauliList contains commuting Pauli operators.

**Return type**

[list](https://docs.python.org/3/library/stdtypes.html#list)\[[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")]

### group\_qubit\_wise\_commuting

`group_qubit_wise_commuting()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1212-L1218)

Partition a PauliList into sets of mutually qubit-wise commuting Pauli strings.

**Returns**

List of PauliLists where each PauliList contains commutable Pauli operators.

**Return type**

[list](https://docs.python.org/3/library/stdtypes.html#list)\[[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")]

### input\_dims

`input_dims(qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/base_operator.py#L135-L137)

Return tuple of input dimension for specified subsystems.

### insert

`insert(ind, value, qubit=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L412-L474)

Insert Paulis into the table.

When inserting qubits the qubit index is the same as the column index of the underlying `X` and `Z` arrays.

**Parameters**

- **ind** ([*int*](https://docs.python.org/3/library/functions.html#int)) – index to insert at.
- **value** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – values to insert.
- **qubit** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – if `True` insert qubit columns, otherwise insert Pauli rows (Default: `False`).

**Returns**

the resulting table with the entries inserted.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the insertion index is invalid.

### inverse

`inverse()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L832-L834)

Return the inverse of each Pauli in the list.

### label\_iter

`label_iter()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1063-L1083)

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 [`to_labels()`](#qiskit.quantum_info.PauliList.to_labels "qiskit.quantum_info.PauliList.to_labels") method.

**Returns**

label iterator object for the PauliList.

**Return type**

LabelIterator

### matrix\_iter

`matrix_iter(sparse=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1085-L1112)

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 [`to_matrix()`](#qiskit.quantum_info.PauliList.to_matrix "qiskit.quantum_info.PauliList.to_matrix") method.

**Parameters**

**sparse** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – optionally return sparse CSR matrices if `True`, otherwise return Numpy array matrices (Default: `False`)

**Returns**

matrix iterator object for the PauliList.

**Return type**

MatrixIterator

### noncommutation\_graph

`noncommutation_graph(qubit_wise)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1168-L1188)

Create the non-commutation graph of this PauliList.

This transforms the measurement operator grouping problem into graph coloring problem. The constructed graph contains one node for each Pauli. The nodes will be connecting for any two Pauli terms that do \_not\_ commute.

**Parameters**

**qubit\_wise** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – whether the commutation rule is applied to the whole operator, or on a per-qubit basis.

**Returns**

**the non-commutation graph with nodes for each Pauli and edges**

indicating a non-commutation relation. Each node will hold the index of the Pauli term it corresponds to in its data. The edges of the graph hold no data.

**Return type**

[rustworkx.PyGraph](https://www.rustworkx.org/apiref/rustworkx.PyGraph.html#rustworkx.PyGraph)

### output\_dims

`output_dims(qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/base_operator.py#L139-L141)

Return tuple of output dimension for specified subsystems.

### power

`power(n)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/mixins/group.py#L154-L174)

Return the composition of an operator with itself n times.

**Parameters**

**n** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the number of times to compose with self (n>0).

**Returns**

the n-times composed operator.

**Return type**

[Clifford](/docs/api/qiskit/qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.

### reshape

`reshape(input_dims=None, output_dims=None, num_qubits=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/base_operator.py#L106-L133)

Return a shallow copy with reshaped input and output subsystem dimensions.

**Parameters**

- **input\_dims** (*None or* [*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple)) – new subsystem input dimensions. If None the original input dims will be preserved \[Default: None].
- **output\_dims** (*None or* [*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple)) – new subsystem output dimensions. If None the original output dims will be preserved \[Default: None].
- **num\_qubits** (*None or* [*int*](https://docs.python.org/3/library/functions.html#int)) – reshape to an N-qubit operator \[Default: None].

**Returns**

returns self with reshaped input and output dimensions.

**Return type**

BaseOperator

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

### sort

`sort(weight=False, phase=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L539-L597)

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

```python
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)
```

```text
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']
```

**Parameters**

- **weight** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – optionally sort by weight if `True` (Default: `False`).
- **phase** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Optionally sort by phase before weight or order (Default: `False`).

**Returns**

a sorted copy of the original table.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

### tensor

`tensor(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L671-L687)

Return the tensor product with each Pauli in the list.

**Parameters**

**other** ([*PauliList*](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")) – another PauliList.

**Returns**

the list of tensor product Paulis.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if other cannot be converted to a PauliList, does not have either 1 or the same number of Paulis as the current list.

### to\_labels

`to_labels(array=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L961-L1007)

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.

| Label | Symplectic | Matrix                                          |
| ----- | ---------- | ----------------------------------------------- |
| `"I"` | $[0, 0]$   | $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$  |
| `"X"` | $[1, 0]$   | $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$  |
| `"Y"` | $[1, 1]$   | $\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}$ |
| `"Z"` | $[0, 1]$   | $\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ |

**Parameters**

**array** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – return a Numpy array if `True`, otherwise return a list (Default: `False`).

**Returns**

The rows of the PauliList in label form.

**Return type**

[list](https://docs.python.org/3/library/stdtypes.html#list) or [array](/docs/api/qiskit/qiskit.primitives.BitArray#array "qiskit.primitives.BitArray.array")

### to\_matrix

`to_matrix(sparse=False, array=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L1009-L1057)

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.

| Label | Symplectic | Matrix                                          |
| ----- | ---------- | ----------------------------------------------- |
| `"I"` | $[0, 0]$   | $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$  |
| `"X"` | $[1, 0]$   | $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$  |
| `"Y"` | $[1, 1]$   | $\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}$ |
| `"Z"` | $[0, 1]$   | $\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ |

**Parameters**

- **sparse** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – if `True` return sparse CSR matrices, otherwise return dense Numpy arrays (Default: `False`).
- **array** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – return as rank-3 numpy array if `True`, otherwise return a list of Numpy arrays (Default: `False`).

**Returns**

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`.

**Return type**

[list](https://docs.python.org/3/library/stdtypes.html#list)

### transpose

`transpose()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L824-L826)

Return the transpose of each Pauli in the list.

### unique

`unique(return_index=False, return_counts=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/operators/symplectic/pauli_list.py#L599-L665)

Return unique Paulis from the table.

**Example**

```python
from qiskit.quantum_info.operators import PauliList

pt = PauliList(['X', 'Y', '-X', 'I', 'I', 'Z', 'X', 'iZ'])
unique = pt.unique()
print(unique)
```

```text
['X', 'Y', '-X', 'I', 'Z', 'iZ']
```

**Parameters**

- **return\_index** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If `True`, also return the indices that result in the unique array. (Default: `False`)
- **return\_counts** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If `True`, also return the number of times each unique item appears in the table.

**Returns**

**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`.

**Return type**

[PauliList](#qiskit.quantum_info.PauliList "qiskit.quantum_info.PauliList")