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__
__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. |
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
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
adjoint()
Return the adjoint of the operator.
atol
The default absolute tolerance parameter for float comparisons.
coeffs
Return the Pauli coefficients.
compose
compose(other, qargs=None, front=False)
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
Raises
- QiskitError – if other cannot be converted to an Operator or has
- incompatible dimensions. –
conjugate
conjugate()
Return the conjugate of the operator.
copy
copy()
Make a deep copy of current operator.
dim
Return tuple (input_shape, output_shape).
dot
dot(other, qargs=None)
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
Raises
- QiskitError – if other cannot be converted to an Operator or has
- incompatible dimensions. –
expand
expand(other)
Return the tensor product operator other ⊗ self.
Parameters
other (SparsePauliOp) – an operator object.
Returns
the tensor product operator other ⊗ self.
Return type
Raises
QiskitError – if other cannot be converted to a SparsePauliOp operator.
from_list
static from_list(obj)
Construct from a list [(pauli_str, coeffs)]
from_operator
static from_operator(obj, atol=None, rtol=None)
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
Raises
QiskitError – if the input operator is not an N-qubit operator.
input_dims
input_dims(qargs=None)
Return tuple of input dimension for specified subsystems.
is_unitary
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) – 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
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
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
multiply
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.
num_qubits
Return the number of qubits if a N-qubit operator or None otherwise.
output_dims
output_dims(qargs=None)
Return tuple of output dimension for specified subsystems.
power
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.
qargs
Return the qargs for the operator.
reshape
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.
rtol
The relative tolerance parameter for float comparisons.
set_atol
classmethod set_atol(value)
Set the class default absolute tolerance parameter for float comparisons.
DEPRECATED: use operator.atol = value instead
set_rtol
classmethod set_rtol(value)
Set the class default relative tolerance parameter for float comparisons.
DEPRECATED: use operator.rtol = value instead
simplify
simplify(atol=None, rtol=None)
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
size
The number of Pauli of Pauli terms in the operator.
subtract
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
table
Return the the PauliTable.
tensor
tensor(other)
Return the tensor product operator self ⊗ other.
Parameters
other (SparsePauliOp) – a operator subclass object.
Returns
the tensor product operator self ⊗ other.
Return type
Raises
QiskitError – if other cannot be converted to a SparsePauliOp operator.
to_list
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
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
to_operator()
Convert to a matrix Operator object
transpose
transpose()
Return the transpose of the operator.