SparsePauliOp
class SparsePauliOp(data, coeffs=None, *, ignore_pauli_phase=False, copy=True)
Bases: qiskit.quantum_info.operators.linear_op.LinearOp
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 PauliList 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 PauliList object and can be accessed using the paulis 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 (PauliList orSparsePauliOp orPauliTable orPauli or list or str) – Pauli list of terms. A list of Pauli strings or a Pauli string is also allowed.
-
coeffs (np.ndarray) –
complex coefficients for Pauli terms.
NoteIf
datais aSparsePauliOpandcoeffsis notNone, the value of theSparsePauliOp.coeffswill be ignored, and only the passed keyword argumentcoeffswill be used. -
ignore_pauli_phase (bool) – if true, any
phasecomponent of a givenPauliListwill be assumed to be zero. This is more efficient in cases where aPauliListhas been constructed purely for this object, and it is already known that the phases in the ZX-convention are zero. It only makes sense to pass this option when givingPauliListdata. (Default: False) -
copy (bool) – copy the input data if True, otherwise assign it directly, if possible. (Default: True)
Raises
QiskitError – If the input data or coeffs are invalid.
Methods
adjoint
SparsePauliOp.adjoint()
Return the adjoint of the Operator.
chop
SparsePauliOp.chop(tol=1e-14)
Set real and imaginary parts of the coefficients to 0 if < tol in magnitude.
For example, the operator representing 1+1e-17j X + 1e-17 Y with a tolerance larger than 1e-17 will be reduced to 1 X whereas SparsePauliOp.simplify() would return 1+1e-17j X.
If a both the real and imaginary part of a coefficient is 0 after chopping, the corresponding Pauli is removed from the operator.
Parameters
tol (float) – The absolute tolerance to check whether a real or imaginary part should be set to 0.
Returns
This operator with chopped coefficients.
Return type
compose
SparsePauliOp.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
SparsePauliOp.conjugate()
Return the conjugate of the SparsePauliOp.
copy
SparsePauliOp.copy()
Make a deep copy of current operator.
dot
SparsePauliOp.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
equiv
SparsePauliOp.equiv(other)
Check if two SparsePauliOp operators are equivalent.
Parameters
other (SparsePauliOp) – an operator object.
Returns
True if the operator is equivalent to self.
Return type
bool
expand
SparsePauliOp.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 SparsePauliOp.from_list(obj)
Construct from a list of Pauli strings and coefficients.
For example, the 5-qubit Hamiltonian
can be constructed as
# via tuples and the full Pauli string
op = SparsePauliOp.from_list([("XIIZI", 1), ("IYIIY", 2)])Parameters
obj (Iterable[Tuple[str, complex]]) – The list of 2-tuples specifying the Pauli terms.
Returns
The SparsePauliOp representation of the Pauli terms.
Return type
Raises
QiskitError – If the list of Paulis is empty.
from_operator
static SparsePauliOp.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.
from_sparse_list
static SparsePauliOp.from_sparse_list(obj, num_qubits)
Construct from a list of local Pauli strings and coefficients.
Each list element is a 3-tuple of a local Pauli string, indices where to apply it, and a coefficient.
For example, the 5-qubit Hamiltonian
can be constructed as
# via triples and local Paulis with indices
op = SparsePauliOp.from_sparse_list([("ZX", [1, 4], 1), ("YY", [0, 3], 2)], num_qubits=5)
# equals the following construction from "dense" Paulis
op = SparsePauliOp.from_list([("XIIZI", 1), ("IYIIY", 2)])Parameters
- obj (Iterable[Tuple[str, List[int], complex]]) – The list 3-tuples specifying the Paulis.
- num_qubits (int) – The number of qubits of the operator.
Returns
The SparsePauliOp representation of the Pauli terms.
Return type
Raises
- QiskitError – If the list of Paulis is empty.
- QiskitError – If the number of qubits is incompatible with the indices of the Pauli terms.
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) – 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
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 PauliList.
Return type
MatrixIterator
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
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, 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.
simplify
SparsePauliOp.simplify(atol=None, rtol=None)
Simplify PauliList 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
sum
static SparsePauliOp.sum(ops)
Sum of SparsePauliOps.
This is a specialized version of the builtin sum function for SparsePauliOp with smaller overhead.
Parameters
ops (list[SparsePauliOp]) – a list of SparsePauliOps.
Returns
the SparsePauliOp representing the sum of the input list.
Return type
Raises
- QiskitError – if the input list is empty.
- QiskitError – if the input list includes an object that is not SparsePauliOp.
- QiskitError – if the numbers of qubits of the objects in the input list do not match.
tensor
SparsePauliOp.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
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 PauliList.
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 SparsePauliOp.
Attributes
atol
Default value: 1e-08
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.
paulis
Return the the PauliList.
qargs
Return the qargs for the operator.
rtol
Default value: 1e-05
settings
Return settings.
Return type
Dict
size
The number of Pauli of Pauli terms in the operator.
table
DEPRECATED - Return the the PauliTable.