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# qiskit.quantum_info.SparsePauliOp¶

class SparsePauliOp(data, coeffs=None)[source]

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)[source]

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. add(other) Return the linear operator self + other. Return the adjoint of the operator. compose(other[, qargs, front]) Return the composition channel self∘other. Return the conjugate of the operator. Make a deep copy of current operator. dot(other[, qargs]) Return the composition channel self∘other. expand(other) Return the tensor product operator other ⊗ self. 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. Return a label representation iterator. matrix_iter([sparse]) Return a matrix representation iterator. multiply(other) Return the linear operator other * self. output_dims([qargs]) Return tuple of output dimension for specified subsystems. Return the compose of a operator with itself n times. reshape([input_dims, output_dims]) Return a shallow copy with reshaped input and output subsystem dimensions. set_atol(value) Set the class default absolute tolerance parameter for float comparisons. set_rtol(value) Set the class default relative tolerance parameter for float comparisons. simplify([atol, rtol]) Simplify PauliTable by combining duplicaties and removing zeros. subtract(other) Return the linear operator self - other. tensor(other) Return the tensor product operator self ⊗ other. to_list([array]) Convert to a list Pauli string labels and coefficients. to_matrix([sparse]) Convert to a dense or sparse matrix. Convert to a matrix Operator object Return the transpose of the operator.

Attributes

 atol The 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 The relative tolerance parameter for float comparisons. size The number of Pauli of Pauli terms in the operator. table Return the the PauliTable.
add(other)

Return the linear operator self + other.

DEPRECATED: use operator + other instead.

Parameters

other (BaseOperator) – an operator object.

Returns

the operator self + other.

Return type

BaseOperator

adjoint()[source]

Return the adjoint of the operator.

property atol

The default absolute tolerance parameter for float comparisons.

property coeffs

Return the Pauli coefficients.

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

Return the composition channel self∘other.

Parameters
• other (SparsePauliOp) – an operator object.

• qargs (list or None) – a list of subsystem positions to compose other on.

• front (bool or None) – If False compose in standard order other(self(input)) otherwise compose in reverse order self(other(input)) [default: False]

Returns

The composed operator.

Return type

SparsePauliOp

Raises
• QiskitError – if other cannot be converted to an Operator or has

• incompatible dimensions.

conjugate()[source]

Return the conjugate of the operator.

copy()

Make a deep copy of current operator.

property dim

Return tuple (input_shape, output_shape).

dot(other, qargs=None)[source]

Return the composition channel self∘other.

Parameters
• other (SparsePauliOp) – an operator object.

• qargs (list or None) – a list of subsystem positions to compose other on.

Returns

The composed operator.

Return type

SparsePauliOp

Raises
• QiskitError – if other cannot be converted to an Operator or has

• incompatible dimensions.

expand(other)[source]

Return the tensor product operator other ⊗ self.

Parameters

other (SparsePauliOp) – an operator object.

Returns

the tensor product operator other ⊗ self.

Return type

SparsePauliOp

Raises

QiskitError – if other cannot be converted to a SparsePauliOp operator.

static from_list(obj)[source]

Construct from a list [(pauli_str, coeffs)]

static from_operator(obj, atol=None, rtol=None)[source]

Construct from an Operator objector.

Note that the cost of this contruction 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) – Optinoal. 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)[source]

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) – Optinoal. 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()[source]

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)[source]

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

multiply(other)

Return the linear operator other * self.

DEPRECATED: use other * operator instead.

Parameters

other (complex) – a complex number.

Returns

the linear operator other * self.

Return type

BaseOperator

Raises

NotImplementedError – if subclass does not support multiplication.

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

BaseOperator

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)

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

Arg:
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].

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

The relative tolerance parameter for float comparisons.

classmethod set_atol(value)

Set the class default absolute tolerance parameter for float comparisons.

DEPRECATED: use operator.atol = value instead

classmethod set_rtol(value)

Set the class default relative tolerance parameter for float comparisons.

DEPRECATED: use operator.rtol = value instead

simplify(atol=None, rtol=None)[source]

Simplify PauliTable by combining duplicaties and removing zeros.

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

• rtol (float) – Optinoal. 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.

subtract(other)

Return the linear operator self - other.

DEPRECATED: use operator - other instead.

Parameters

other (BaseOperator) – an operator object.

Returns

the operator self - other.

Return type

BaseOperator

property table

Return the the PauliTable.

tensor(other)[source]

Return the tensor product operator self ⊗ other.

Parameters

other (SparsePauliOp) – a operator subclass object.

Returns

the tensor product operator self ⊗ other.

Return type

SparsePauliOp

Raises

QiskitError – if other cannot be converted to a SparsePauliOp operator.

to_list(array=False)[source]

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)[source]

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()[source]

Convert to a matrix Operator object

transpose()[source]

Return the transpose of the operator.