qiskit.quantum_info.SparsePauliOp¶

class SparsePauliOp(data, coeffs=None)[Quellcode]¶

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.

Parameter

data (PauliTable) – Pauli table of terms.
coeffs (np.ndarray) – complex coefficients for Pauli terms.

Verursacht

QiskitError – If the input data or coeffs are invalid.

__init__(data, coeffs=None)[Quellcode]¶

Initialize an operator object.

Parameter

data (PauliTable) – Pauli table of terms.
coeffs (np.ndarray) – complex coefficients for Pauli terms.

Verursacht

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.
`adjoint`()	Return the adjoint of the operator.
`compose`(other[, qargs, front])	Return the composition channel self∘other.
`conjugate`()	Return the conjugate of the operator.
`copy`()	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.
`label_iter`()	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.
`power`(n)	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.
`to_operator`()	Convert to a matrix Operator object
`transpose`()	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.

Parameter: other (BaseOperator) – an operator object.
Rückgabe: the operator self + other.
Rückgabetyp: BaseOperator

adjoint()[Quellcode]¶: 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)[Quellcode]¶

Return the composition channel self∘other.

Parameter

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]

Rückgabe

The composed operator.

Rückgabetyp

SparsePauliOp

Verursacht

QiskitError – if other cannot be converted to an Operator or has
incompatible dimensions. –

conjugate()[Quellcode]¶: 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)[Quellcode]¶

Return the composition channel self∘other.

Parameter

other (SparsePauliOp) – an operator object.
qargs (list or None) – a list of subsystem positions to compose other on.

Rückgabe

The composed operator.

Rückgabetyp

SparsePauliOp

Verursacht

QiskitError – if other cannot be converted to an Operator or has
incompatible dimensions. –

expand(other)[Quellcode]¶

Return the tensor product operator other ⊗ self.

Parameter: other (SparsePauliOp) – an operator object.
Rückgabe: the tensor product operator other ⊗ self.
Rückgabetyp: SparsePauliOp
Verursacht: QiskitError – if other cannot be converted to a SparsePauliOp operator.

static from_list(obj)[Quellcode]¶: Construct from a list [(pauli_str, coeffs)]

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

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.

Parameter

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).

Rückgabe

the SparsePauliOp representation of the operator.

Rückgabetyp

SparsePauliOp

Verursacht

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)[Quellcode]¶

Return True if operator is a unitary matrix.

Parameter

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).

Rückgabe

True if the operator is unitary, False otherwise.

Rückgabetyp

bool

label_iter()[Quellcode]¶

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.

Rückgabe: label iterator object for the PauliTable.
Rückgabetyp: LabelIterator

matrix_iter(sparse=False)[Quellcode]¶

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.

Parameter: sparse (bool) – optionally return sparse CSR matrices if True, otherwise return Numpy array matrices (Default: False)
Rückgabe: matrix iterator object for the PauliTable.
Rückgabetyp: MatrixIterator

multiply(other)¶

Return the linear operator other * self.

DEPRECATED: use other * operator instead.

Parameter: other (complex) – a complex number.
Rückgabe: the linear operator other * self.
Rückgabetyp: BaseOperator
Verursacht: 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.

Parameter: n (int) – the number of times to compose with self (n>0).
Rückgabe: the n-times composed operator.
Rückgabetyp: BaseOperator
Verursacht: 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].

Rückgabe: returns self with reshaped input and output dimensions.
Rückgabetyp: BaseOperator
Verursacht: 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)[Quellcode]¶

Simplify PauliTable by combining duplicaties and removing zeros.

Parameter

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).

Rückgabe

the simplified SparsePauliOp operator.

Rückgabetyp

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.

Parameter: other (BaseOperator) – an operator object.
Rückgabe: the operator self - other.
Rückgabetyp: BaseOperator

property table¶: Return the the PauliTable.

tensor(other)[Quellcode]¶

Return the tensor product operator self ⊗ other.

Parameter: other (SparsePauliOp) – a operator subclass object.
Rückgabe: the tensor product operator self ⊗ other.
Rückgabetyp: SparsePauliOp
Verursacht: QiskitError – if other cannot be converted to a SparsePauliOp operator.

to_list(array=False)[Quellcode]¶

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.

Parameter: array (bool) – return a Numpy array if True, otherwise return a list (Default: False).
Rückgabe: List of pairs (label, coeff) for rows of the PauliTable.
Rückgabetyp: list or array

to_matrix(sparse=False)[Quellcode]¶

Convert to a dense or sparse matrix.

Parameter: sparse (bool) – if True return a sparse CSR matrix, otherwise return dense Numpy array (Default: False).
Rückgabe: A dense matrix if sparse=False. csr_matrix: A sparse matrix in CSR format if sparse=True.
Rückgabetyp: array

to_operator()[Quellcode]¶: Convert to a matrix Operator object

transpose()[Quellcode]¶: Return the transpose of the operator.