SparsePauliOp

class SparsePauliOp(data, coeffs=None, *, ignore_pauli_phase=False, copy=True)

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Bases: qiskit.quantum_info.operators.linear_op.LinearOp

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 PauliList 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 PauliList object and can be accessed using the paulis attribute. The coefficients are stored as a complex Numpy array vector and can be accessed using the coeffs attribute.

Initialize an operator object.

Parameters

$data (PauliList or SparsePauliOp or PauliTable or Pauli or list or str) - Pauli list of terms. A list of Pauli strings or a Pauli string is also allowed.$
$coeffs (np.ndarray) -$ $complex coefficients for Pauli terms.$
Note
$If data is a SparsePauliOp and coeffs is not None, the value of the SparsePauliOp.coeffs will be ignored, and only the passed keyword argument coeffs will be used.$
$ignore_pauli_phase (bool) - if true, any phase component of a given PauliList will be assumed to be zero. This is more efficient in cases where a PauliList has been constructed purely for this object, and it is already known that the phases in the ZX-convention are zero. It only makes sense to pass this option when giving PauliList data. (Default: False)$
$copy (bool) - copy the input data if True, otherwise assign it directly, if possible. (Default: True)$

Raises

QiskitError - If the input data or coeffs are invalid.

Methods

adjoint

SparsePauliOp.adjoint()

Return the adjoint of the Operator.

compose

SparsePauliOp.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

SparsePauliOp.conjugate()

Return the conjugate of the SparsePauliOp.

copy

SparsePauliOp.copy()

Make a deep copy of current operator.

dot

SparsePauliOp.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

SparsePauliOp.expand(other)

Return the reverse-order tensor product with another SparsePauliOp.

Parameters

other (SparsePauliOp) - a SparsePauliOp object.

Returns

b \otimes a

b

Return type

SparsePauliOp

from_list

static SparsePauliOp.from_list(obj)

Construct from a list [(pauli_str, coeffs)]

from_operator

static SparsePauliOp.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

SparsePauliOp.input_dims(qargs=None)

Return tuple of input dimension for specified subsystems.

is_unitary

SparsePauliOp.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

SparsePauliOp.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

SparsePauliOp.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 PauliList.

Return type

MatrixIterator

output_dims

SparsePauliOp.output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

power

SparsePauliOp.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.

reshape

SparsePauliOp.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.

simplify

SparsePauliOp.simplify(atol=None, rtol=None)

Simplify PauliList 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

sum

static SparsePauliOp.sum(ops)

Sum of SparsePauliOps.

This is a specialized version of the builtin sum function for SparsePauliOp with smaller overhead.

Parameters

ops (list[SparsePauliOp]) - a list of SparsePauliOps.

Returns

the SparsePauliOp representing the sum of the input list.

Return type

SparsePauliOp

Raises

QiskitError – if the input list is empty.
QiskitError – if the input list includes an object that is not SparsePauliOp.
QiskitError – if the numbers of qubits of the objects in the input list do not match.

tensor

SparsePauliOp.tensor(other)

Return the tensor product with another SparsePauliOp.

Parameters

other (SparsePauliOp) - a SparsePauliOp object.

Returns

a \otimes b

b

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

SparsePauliOp.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 PauliList.

Return type

list or array

to_matrix

SparsePauliOp.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

SparsePauliOp.to_operator()

Convert to a matrix Operator object

transpose

SparsePauliOp.transpose()

Return the transpose of the SparsePauliOp.

Attributes

atol

Default value: 1e-08

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.

paulis

Return the the PauliList.

qargs

Return the qargs for the operator.

rtol

Default value: 1e-05

settings

Return settings.

Return type

Dict

size

The number of Pauli of Pauli terms in the operator.

table

DEPRECATED - Return the the PauliTable.

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