qiskit.quantum_info.SparsePauliOp

class SparsePauliOp(data, coeffs=None)

Sparse N-qubit operator in a Pauli basis representation.

This is a sparse representation of an N-qubit matrix Operator in terms of N-qubit PauliTable and complex coefficients.

It can be used for performing operator arithmetic for hundred of qubits if the number of non-zero Pauli basis terms is sufficiently small.

The Pauli basis components are stored as a PauliTable object and can be accessed using the table attribute. The coefficients are stored as a complex Numpy array vector and can be accessed using the coeffs attribute.

Initialize an operator object.

Parameters

• data (PauliTable) – Pauli table of terms.

• coeffs (np.ndarray) – complex coefficients for Pauli terms.

Raises

QiskitError – If the input data or coeffs are invalid.

__init__(data, coeffs=None)

Initialize an operator object.

Parameters

• data (PauliTable) – Pauli table of terms.

• coeffs (np.ndarray) – complex coefficients for Pauli terms.

Raises

QiskitError – If the input data or coeffs are invalid.

Methods

__init__(data[, coeffs])	Initialize an operator object.
adjoint()	Return the adjoint of the Operator.
compose(other[, qargs, front])	Return the operator composition with another SparsePauliOp.
conjugate()	Return the conjugate of the SparsePauliOp.
copy()	Make a deep copy of current operator.
dot(other[, qargs])	Return the right multiplied operator self * other.
expand(other)	Return the reverse-order tensor product with another SparsePauliOp.
from_list(obj)	Construct from a list [(pauli_str, coeffs)]
from_operator(obj[, atol, rtol])	Construct from an Operator objector.
input_dims([qargs])	Return tuple of input dimension for specified subsystems.
is_unitary([atol, rtol])	Return True if operator is a unitary matrix.
label_iter()	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.
simplify([atol, rtol])	Simplify PauliTable by combining duplicates and removing zeros.
tensor(other)	Return the tensor product with another SparsePauliOp.
to_list([array])	Convert to a list Pauli string labels and coefficients.
to_matrix([sparse])	Convert to a dense or sparse matrix.
to_operator()	Convert to a matrix Operator object
transpose()	Return the transpose of the SparsePauliOp.

Attributes

atol	Default absolute tolerance parameter for float comparisons.
coeffs	Return the Pauli coefficients.
dim	Return tuple (input_shape, output_shape).
num_qubits	Return the number of qubits if a N-qubit operator or None otherwise.
qargs	Return the qargs for the operator.
rtol	Default relative tolerance parameter for float comparisons.
size	The number of Pauli of Pauli terms in the operator.
table	Return the the PauliTable.

adjoint()

Return the adjoint of the Operator.

property atol

Default absolute tolerance parameter for float comparisons.

property coeffs

Return the Pauli coefficients.

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

Return the operator composition with another SparsePauliOp.

Parameters

• other (SparsePauliOp) – a SparsePauliOp object.

• qargs (list or None) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

• front (bool) – If True compose using right operator multiplication, instead of left multiplication [default: False].

Returns

The composed SparsePauliOp.

Return type

SparsePauliOp

Raises

QiskitError – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.

Note

Composition (&) by default is defined as left matrix multiplication for matrix operators, while dot() is defined as right matrix multiplication. That is that A & B == A.compose(B) is equivalent to B.dot(A) when A and B are of the same type.

Setting the front=True kwarg changes this to right matrix multiplication and is equivalent to the dot() method A.dot(B) == A.compose(B, front=True).

conjugate()

Return the conjugate of the SparsePauliOp.

copy()

Make a deep copy of current operator.

property dim

Return tuple (input_shape, output_shape).

dot(other, qargs=None)

Return the right multiplied operator self * other.

Parameters

• other (Operator) – an operator object.

• qargs (list or None) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

Returns

The right matrix multiplied Operator.

Return type

Operator

expand(other)

Return the reverse-order tensor product with another SparsePauliOp.

Parameters

other (SparsePauliOp) – a SparsePauliOp object.

Returns

the tensor product \(b \otimes a\), where \(a\)

is the current SparsePauliOp, and \(b\) is the other SparsePauliOp.

Return type

SparsePauliOp

static from_list(obj)

Construct from a list [(pauli_str, coeffs)]

static from_operator(obj, atol=None, rtol=None)

Construct from an Operator objector.

Note that the cost of this construction is exponential as it involves taking inner products with every element of the N-qubit Pauli basis.

Parameters

• obj (Operator) – an N-qubit operator.

• atol (float) – Optional. Absolute tolerance for checking if coefficients are zero (Default: 1e-8).

• rtol (float) – Optional. relative tolerance for checking if coefficients are zero (Default: 1e-5).

Returns

the SparsePauliOp representation of the operator.

Return type

SparsePauliOp

Raises

QiskitError – if the input operator is not an N-qubit operator.

input_dims(qargs=None)

Return tuple of input dimension for specified subsystems.

is_unitary(atol=None, rtol=None)

Return True if operator is a unitary matrix.

Parameters

• atol (float) – Optional. Absolute tolerance for checking if coefficients are zero (Default: 1e-8).

• rtol (float) – Optional. relative tolerance for checking if coefficients are zero (Default: 1e-5).

Returns

True if the operator is unitary, False otherwise.

Return type

bool

label_iter()

Return a label representation iterator.

This is a lazy iterator that converts each term in the SparsePauliOp into a tuple (label, coeff). To convert the entire table to labels use the to_labels() method.

Returns

label iterator object for the PauliTable.

Return type

LabelIterator

matrix_iter(sparse=False)

Return a matrix representation iterator.

This is a lazy iterator that converts each term in the SparsePauliOp into a matrix as it is used. To convert to a single matrix use the to_matrix() method.

Parameters

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

Returns

matrix iterator object for the PauliTable.

Return type

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.

power(n)

Return the compose of a operator with itself n times.

Parameters

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

Returns

the n-times composed operator.

Return type

Pauli

Raises

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.

Parameters

• 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].

Returns

returns self with reshaped input and output dimensions.

Return type

BaseOperator

Raises

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

property rtol

Default relative tolerance parameter for float comparisons.

simplify(atol=None, rtol=None)

Simplify PauliTable by combining duplicates and removing zeros.

Parameters

• atol (float) – Optional. Absolute tolerance for checking if coefficients are zero (Default: 1e-8).

• rtol (float) – Optional. relative tolerance for checking if coefficients are zero (Default: 1e-5).

Returns

the simplified SparsePauliOp operator.

Return type

SparsePauliOp

property size

The number of Pauli of Pauli terms in the operator.

property table

Return the the PauliTable.

tensor(other)

Return the tensor product with another SparsePauliOp.

Parameters

other (SparsePauliOp) – a SparsePauliOp object.

Returns

the tensor product \(a \otimes b\), where \(a\)

is the current SparsePauliOp, and \(b\) is the other SparsePauliOp.

Return type

SparsePauliOp

Note

The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.

to_list(array=False)

Convert to a list Pauli string labels and coefficients.

For operators with a lot of terms converting using the array=True kwarg will be more efficient since it allocates memory for the full Numpy array of labels in advance.

Parameters

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

Returns

List of pairs (label, coeff) for rows of the PauliTable.

Return type

list or array

to_matrix(sparse=False)

Convert to a dense or sparse matrix.

Parameters

sparse (bool) – if True return a sparse CSR matrix, otherwise return dense Numpy array (Default: False).

Returns

A dense matrix if sparse=False. csr_matrix: A sparse matrix in CSR format if sparse=True.

Return type

array

to_operator()

Convert to a matrix Operator object

transpose()

Return the transpose of the SparsePauliOp.