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. |
adjoint() | Return the adjoint of the Operator. |
compose(other[, qargs, front]) | Return the operator composition with another SparsePauliOp. |
conjugate() | Return the conjugate of the SparsePauliOp. |
copy() | Make a deep copy of current operator. |
dot(other[, qargs]) | Return the right multiplied operator self * other. |
expand(other) | Return the reverse-order tensor product with another SparsePauliOp. |
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. |
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, num_qubits]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
simplify([atol, rtol]) | Simplify PauliTable by combining duplicates and removing zeros. |
tensor(other) | Return the tensor product with another SparsePauliOp. |
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 SparsePauliOp. |
Attributes
atol | 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 | Default relative tolerance parameter for float comparisons. |
settings | Return settings. |
size | The number of Pauli of Pauli terms in the operator. |
table | Return the the PauliTable. |
adjoint
adjoint()
Return the adjoint of the Operator.
atol
Default absolute tolerance parameter for float comparisons.
coeffs
Return the Pauli coefficients.
compose
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
Raises
QiskitError – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
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
conjugate()
Return the conjugate of the SparsePauliOp.
copy
copy()
Make a deep copy of current operator.
dim
Return tuple (input_shape, output_shape).
dot
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
expand
expand(other)
Return the reverse-order tensor product with another SparsePauliOp.
Parameters
other (SparsePauliOp) – a SparsePauliOp object.
Returns
the tensor product , where
is the current SparsePauliOp, and is the other SparsePauliOp.
Return type
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 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
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) – 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
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
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
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, 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.
rtol
Default relative tolerance parameter for float comparisons.
settings
Return settings.
Return type
Dict
simplify
simplify(atol=None, rtol=None)
Simplify PauliTable 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
size
The number of Pauli of Pauli terms in the operator.
table
Return the the PauliTable.
tensor
tensor(other)
Return the tensor product with another SparsePauliOp.
Parameters
other (SparsePauliOp) – a SparsePauliOp object.
Returns
the tensor product , where
is the current SparsePauliOp, and is the other SparsePauliOp.
Return type
The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.
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 SparsePauliOp.