# qiskit.quantum_info.StabilizerTable¶

class StabilizerTable(data, phase=None)[소스]

Symplectic representation of a list Stabilizer matrices.

Symplectic Representation

The symplectic representation of a single-qubit Stabilizer matrix is a pair of boolean values $$[x, z]$$ and a boolean phase p such that the Stabilizer matrix is given by $$S = (-1)^p \sigma_z^z.\sigma_x^x$$. The correspondence between labels, symplectic representation, stabilizer matrices, and Pauli matrices for the single-qubit case is shown in the following table.

Table 11 Table 1: Stabilizer Representations

Label

Phase

Symplectic

Matrix

Pauli

"+I"

0

$$[0, 0]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$I$$

"-I"

1

$$[0, 0]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$-I$$

"X"

0

$$[1, 0]$$

$$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$

$$X$$

"-X"

1

$$[1, 0]$$

$$\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$$

$$-X$$

"Y"

0

$$[1, 1]$$

$$\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$$

$$iY$$

"-Y"

1

$$[1, 1]$$

$$\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$$

$$-iY$$

"Z"

0

$$[0, 1]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$Z$$

"-Z"

1

$$[0, 1]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$-Z$$

Internally this is stored as a length N boolean phase vector $$[p_{N-1}, ..., p_{0}]$$ and a PauliTable $$M \times 2N$$ boolean matrix:

$\begin{split}\left(\begin{array}{ccc|ccc} x_{0,0} & ... & x_{0,N-1} & z_{0,0} & ... & z_{0,N-1} \\ x_{1,0} & ... & x_{1,N-1} & z_{1,0} & ... & z_{1,N-1} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ x_{M-1,0} & ... & x_{M-1,N-1} & z_{M-1,0} & ... & z_{M-1,N-1} \end{array}\right)\end{split}$

where each row is a block vector $$[X_i, Z_i]$$ with $$X_i = [x_{i,0}, ..., x_{i,N-1}]$$, $$Z_i = [z_{i,0}, ..., z_{i,N-1}]$$ 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 from_labels(), and converted to a list of labels or a list of matrices using to_labels() and 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 dot() method will return the output for row.dot(col) = row.col, while the compose() will return row.compose(col) = col.row from the above table.

Note that while this dot product is different to the matrix product of the PauliTable, it does not change the commutation structure of elements. Hence 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 $$X_i, Z_i$$ 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 $$x=[1, 0]$$, $$z=[0, 1]$$.

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 phase and array properties respectively. The sub-arrays for only the X or Z blocks can be accessed using the X and Z properties respectively.

The Pauli part of the Stabilizer table can be viewed and accessed as a PauliTable object using the 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 label_iter() and matrix_iter() methods.

참조

1. S. Aaronson, D. Gottesman, Improved Simulation of Stabilizer Circuits, Phys. Rev. A 70, 052328 (2004). arXiv:quant-ph/0406196

Initialize the StabilizerTable.

매개변수
• data (array or str or PauliTable) – input PauliTable data.

• phase (array or bool or None) – optional phase vector for input data (Default: None).

예외

QiskitError – if input array or phase vector has an invalid shape.

The input array is not copied so multiple Pauli and Stabilizer tables can share the same underlying array.

__init__(data, phase=None)[소스]

Initialize the StabilizerTable.

매개변수
• data (array or str or PauliTable) – input PauliTable data.

• phase (array or bool or None) – optional phase vector for input data (Default: None).

예외

QiskitError – if input array or phase vector has an invalid shape.

The input array is not copied so multiple Pauli and Stabilizer tables can share the same underlying array.

Methods

 __init__(data[, phase]) Initialize the StabilizerTable. adjoint() Return the adjoint of the Operator. anticommutes_with_all(other) Return indexes of rows that commute other. argsort([weight]) Return indices for sorting the rows of the PauliTable. commutes(pauli) Return list of commutation properties for each row with a Pauli. commutes_with_all(other) Return indexes of rows that commute other. compose(other[, qargs, front]) Return the compose output product of two tables. Not implemented. copy() Return a copy of the StabilizerTable. delete(ind[, qubit]) Return a copy with Stabilizer rows deleted from table. dot(other[, qargs]) Return the dot output product of two tables. expand(other) Return the expand output product of two tables. from_labels(labels) Construct a StabilizerTable from a list of Pauli stabilizer strings. input_dims([qargs]) Return tuple of input dimension for specified subsystems. insert(ind, value[, qubit]) Insert stabilizers’s into the table. Return a label representation iterator. matrix_iter([sparse]) Return a matrix representation iterator. output_dims([qargs]) Return tuple of output dimension for specified subsystems. power(n) Return the compose of a operator with itself n times. reshape([input_dims, output_dims, num_qubits]) Return a shallow copy with reshaped input and output subsystem dimensions. sort([weight]) Sort the rows of the table. tensor(other) Return the tensor output product of two tables. to_labels([array]) Convert a StabilizerTable to a list Pauli stabilizer string labels. to_matrix([sparse, array]) Convert to a list or array of Stabilizer matrices. Not implemented. unique([return_index, return_counts]) Return unique stabilizers from the table.

Attributes

 X The X block of the array. Z The Z block of the array. array The underlying boolean array. dim Return tuple (input_shape, output_shape). num_qubits Return the number of qubits if a N-qubit operator or None otherwise. pauli Return PauliTable phase Return phase vector qargs Return the qargs for the operator. shape The full shape of the array() size The number of Pauli rows in the table.
property X

The X block of the array.

property Z

The Z block of the array.

Return the adjoint of the Operator.

anticommutes_with_all(other)

Return indexes of rows that commute other.

If other is a multi-row Pauli table the returned vector indexes rows of the current PauliTable that anti-commute with all Pauli’s in other. If no rows satisfy the condition the returned array will be empty.

매개변수

other (PauliTable) – a single Pauli or multi-row PauliTable.

반환값

index array of the anti-commuting rows.

반환 형식

array

argsort(weight=False)[소스]

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.

매개변수

weight (bool) – optionally sort by weight if True (Default: False).

반환값

the indices for sorting the table.

반환 형식

array

property array

The underlying boolean array.

commutes(pauli)

Return list of commutation properties for each row with a Pauli.

The returned vector is the same length as the size of the table and contains True for rows that commute with the Pauli, and False for the rows that anti-commute.

매개변수

pauli (PauliTable) – a single Pauli row.

반환값

The boolean vector of which rows commute or anti-commute.

반환 형식

array

예외

QiskitError – if input is not a single Pauli row.

commutes_with_all(other)

Return indexes of rows that commute other.

If other is a multi-row Pauli table the returned vector indexes rows of the current PauliTable that commute with all Pauli’s in other. If no rows satisfy the condition the returned array will be empty.

매개변수

other (PauliTable) – a single Pauli or multi-row PauliTable.

반환값

index array of the commuting rows.

반환 형식

array

compose(other, qargs=None, front=False)[소스]

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

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 dot() method.

Example

from qiskit.quantum_info.operators import StabilizerTable

current = StabilizerTable.from_labels(['+I', '-X'])
other =  StabilizerTable.from_labels(['+X', '-Z'])
print(current.compose(other))
StabilizerTable: ['+X', '-Z', '-I', '-Y']
매개변수
• 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).

반환값

the compose outer product table.

반환 형식

StabilizerTable

예외

QiskitError – if other cannot be converted to a StabilizerTable.

conjugate()

Not implemented.

copy()[소스]

Return a copy of the StabilizerTable.

delete(ind, qubit=False)[소스]

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 X and Z arrays.

매개변수
• ind (int or list) – index(es) to delete.

• qubit (bool) – if True delete qubit columns, otherwise delete Stabilizer rows (Default: False).

반환값

the resulting table with the entries removed.

반환 형식

StabilizerTable

예외

QiskitError – if ind is out of bounds for the array size or number of qubits.

property dim

Return tuple (input_shape, output_shape).

dot(other, qargs=None)[소스]

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

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

from qiskit.quantum_info.operators import StabilizerTable

current = StabilizerTable.from_labels(['+I', '-X'])
other =  StabilizerTable.from_labels(['+X', '-Z'])
print(current.dot(other))
StabilizerTable: ['+X', '-Z', '-I', '+Y']
매개변수
• other (StabilizerTable) – another StabilizerTable.

• qargs (None or list) – qubits to apply dot product on (Default: None).

반환값

the dot outer product table.

반환 형식

StabilizerTable

예외

QiskitError – if other cannot be converted to a StabilizerTable.

expand(other)[소스]

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 tensor().

Example

from qiskit.quantum_info.operators import StabilizerTable

current = StabilizerTable.from_labels(['+I', '-X'])
other =  StabilizerTable.from_labels(['-Y', '+Z'])
print(current.expand(other))
StabilizerTable: ['-YI', '+YX', '+ZI', '-ZX']
매개변수

other (StabilizerTable) – another StabilizerTable.

반환값

the expand outer product table.

반환 형식

StabilizerTable

예외

QiskitError – if other cannot be converted to a StabilizerTable.

classmethod from_labels(labels)[소스]

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.

Table 12 Stabilizer Representations

Label

Phase

Symplectic

Matrix

Pauli

"+I"

0

$$[0, 0]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$I$$

"-I"

1

$$[0, 0]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$-I$$

"X"

0

$$[1, 0]$$

$$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$

$$X$$

"-X"

1

$$[1, 0]$$

$$\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$$

$$-X$$

"Y"

0

$$[1, 1]$$

$$\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$$

$$iY$$

"-Y"

1

$$[1, 1]$$

$$\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$$

$$-iY$$

"Z"

0

$$[0, 1]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$Z$$

"-Z"

1

$$[0, 1]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$-Z$$

매개변수

labels (list) – Pauli stabilizer string label(es).

반환값

the constructed StabilizerTable.

반환 형식

StabilizerTable

예외

QiskitError – If the input list is empty or contains invalid Pauli stabilizer strings.

input_dims(qargs=None)

Return tuple of input dimension for specified subsystems.

insert(ind, value, qubit=False)[소스]

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 X and Z arrays.

매개변수
• ind (int) – index to insert at.

• value (StabilizerTable) – values to insert.

• qubit (bool) – if True delete qubit columns, otherwise delete Pauli rows (Default: False).

반환값

the resulting table with the entries inserted.

반환 형식

StabilizerTable

예외

QiskitError – if the insertion index is invalid.

label_iter()[소스]

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() method.

반환값

label iterator object for the StabilizerTable.

반환 형식

LabelIterator

matrix_iter(sparse=False)[소스]

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() method.

매개변수

sparse (bool) – optionally return sparse CSR matrices if True, otherwise return Numpy array matrices (Default: False)

반환값

matrix iterator object for the StabilizerTable.

반환 형식

MatrixIterator

property num_qubits

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

output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

property pauli

Return PauliTable

property phase

Return phase vector

power(n)

Return the compose of a operator with itself n times.

매개변수

n (int) – the number of times to compose with self (n>0).

반환값

the n-times composed operator.

반환 형식

Pauli

예외

QiskitError – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.

property qargs

Return the qargs for the operator.

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

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

매개변수
• input_dims (None or tuple) – new subsystem input dimensions. If None the original input dims will be preserved [Default: None].

• output_dims (None or tuple) – new subsystem output dimensions. If None the original output dims will be preserved [Default: None].

• num_qubits (None or int) – reshape to an N-qubit operator [Default: None].

반환값

returns self with reshaped input and output dimensions.

반환 형식

BaseOperator

예외

QiskitError – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

property shape

The full shape of the array()

property size

The number of Pauli rows in the table.

sort(weight=False)[소스]

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

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)
Initial Ordering
StabilizerTable: ['-IY', '-YI', '-ZY', '+XZ', '+YZ', '+YY', '+ZX', '+ZI', '-XY', '+YI', '+IZ', '-XI', '-XX', '+IY', '-ZX', '-IZ', '-II', '+ZY', '+XI', '-ZZ', '+IX', '-YX', '-YZ', '-IX', '+XY', '-ZI', '+XX', '+ZZ', '+YX', '-XZ', '-YY', '+II']
Lexicographically sorted
StabilizerTable: ['-II', '+II', '+IX', '-IX', '-IY', '+IY', '+IZ', '-IZ', '-XI', '+XI', '-XX', '+XX', '-XY', '+XY', '+XZ', '-XZ', '-YI', '+YI', '-YX', '+YX', '+YY', '-YY', '+YZ', '-YZ', '+ZI', '-ZI', '+ZX', '-ZX', '-ZY', '+ZY', '-ZZ', '+ZZ']
Weight sorted
StabilizerTable: ['-II', '+II', '+IX', '-IX', '-IY', '+IY', '+IZ', '-IZ', '-XI', '+XI', '-YI', '+YI', '+ZI', '-ZI', '-XX', '+XX', '-XY', '+XY', '+XZ', '-XZ', '-YX', '+YX', '+YY', '-YY', '+YZ', '-YZ', '+ZX', '-ZX', '-ZY', '+ZY', '-ZZ', '+ZZ']
매개변수

weight (bool) – optionally sort by weight if True (Default: False).

반환값

a sorted copy of the original table.

반환 형식

StabilizerTable

tensor(other)[소스]

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 tensor().

Example

from qiskit.quantum_info.operators import StabilizerTable

current = StabilizerTable.from_labels(['+I', '-X'])
other =  StabilizerTable.from_labels(['-Y', '+Z'])
print(current.tensor(other))
StabilizerTable: ['-IY', '+IZ', '+XY', '-XZ']
매개변수

other (StabilizerTable) – another StabilizerTable.

반환값

the tensor outer product table.

반환 형식

StabilizerTable

예외

QiskitError – if other cannot be converted to a StabilizerTable.

to_labels(array=False)[소스]

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.

Table 13 Stabilizer Representations

Label

Phase

Symplectic

Matrix

Pauli

"+I"

0

$$[0, 0]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$I$$

"-I"

1

$$[0, 0]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$-I$$

"X"

0

$$[1, 0]$$

$$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$

$$X$$

"-X"

1

$$[1, 0]$$

$$\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$$

$$-X$$

"Y"

0

$$[1, 1]$$

$$\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$$

$$iY$$

"-Y"

1

$$[1, 1]$$

$$\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$$

$$-iY$$

"Z"

0

$$[0, 1]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$Z$$

"-Z"

1

$$[0, 1]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$-Z$$

매개변수

array (bool) – return a Numpy array if True, otherwise return a list (Default: False).

반환값

The rows of the StabilizerTable in label form.

반환 형식

list or array

to_matrix(sparse=False, array=False)[소스]

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.

Table 14 Stabilizer Representations

Label

Phase

Symplectic

Matrix

Pauli

"+I"

0

$$[0, 0]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$I$$

"-I"

1

$$[0, 0]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$-I$$

"X"

0

$$[1, 0]$$

$$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$

$$X$$

"-X"

1

$$[1, 0]$$

$$\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$$

$$-X$$

"Y"

0

$$[1, 1]$$

$$\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$$

$$iY$$

"-Y"

1

$$[1, 1]$$

$$\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$$

$$-iY$$

"Z"

0

$$[0, 1]$$

$$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$$

$$Z$$

"-Z"

1

$$[0, 1]$$

$$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$-Z$$

매개변수
• 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).

반환값

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.

반환 형식

list

transpose()

Not implemented.

unique(return_index=False, return_counts=False)[소스]

Return unique stabilizers from the table.

Example

from qiskit.quantum_info.operators import StabilizerTable

st = StabilizerTable.from_labels(['+X', '+I', '-I', '-X', '+X', '-X', '+I'])
unique = st.unique()
print(unique)
StabilizerTable: ['+X', '+I', '-I', '-X']
매개변수
• 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.

반환값

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.

반환 형식

StabilizerTable