SparsePauliOp
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.
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.
Methods
__call__
SparsePauliOp.__call__(qargs)
Return a clone with qargs set
__getitem__
SparsePauliOp.__getitem__(key)
Return a view of the SparsePauliOp.
__len__
SparsePauliOp.__len__()
Return the size.
__mul__
SparsePauliOp.__mul__(other)
add
SparsePauliOp.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
SparsePauliOp.adjoint()
Return the adjoint of the operator.
compose
SparsePauliOp.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
SparsePauliOp.conjugate()
Return the conjugate of the operator.
copy
SparsePauliOp.copy()
Make a deep copy of current operator.
dot
SparsePauliOp.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
SparsePauliOp.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 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 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
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) – 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
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 PauliTable.
Return type
MatrixIterator
multiply
SparsePauliOp.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.
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
BaseOperator
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)
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.
set_atol
classmethod SparsePauliOp.set_atol(value)
Set the class default absolute tolerance parameter for float comparisons.
set_rtol
classmethod SparsePauliOp.set_rtol(value)
Set the class default relative tolerance parameter for float comparisons.
simplify
SparsePauliOp.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
subtract
SparsePauliOp.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
tensor
SparsePauliOp.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
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 PauliTable.
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 operator.