qiskit.opflow.primitive_ops.PauliOp¶

class
PauliOp
(primitive, coeff=1.0)[source]¶ Class for Operators backed by Terra’s
Pauli
module. Parameters
primitive (
Pauli
) – The Pauli which defines the behavior of the underlying function.coeff (
Union
[complex
,ParameterExpression
]) – A coefficient multiplying the primitive.
 Raises
TypeError – invalid parameters.

__init__
(primitive, coeff=1.0)[source]¶  Parameters
primitive (
Pauli
) – The Pauli which defines the behavior of the underlying function.coeff (
Union
[complex
,ParameterExpression
]) – A coefficient multiplying the primitive.
 Raises
TypeError – invalid parameters.
Methods
__init__
(primitive[, coeff]) type primitive
Pauli
add
(other)Return Operator addition of self and other, overloaded by
+
.adjoint
()Return a new Operator equal to the Operator’s adjoint (conjugate transpose), overloaded by
~
.assign_parameters
(param_dict)Binds scalar values to any Terra
Parameters
in the coefficients or primitives of the Operator, or substitutes oneParameter
for another.bind_parameters
(param_dict)Same as assign_parameters, but maintained for consistency with QuantumCircuit in Terra (which has both assign_parameters and bind_parameters).
compose
(other[, permutation, front])Return Operator Composition between self and other (linear algebrastyle: A@B(x) = A(B(x))), overloaded by
@
.copy
()Return a deep copy of the Operator.
equals
(other)Evaluate Equality between Operators, overloaded by
==
.eval
([front])Evaluate the Operator’s underlying function, either on a binary string or another Operator.
exp_i
()Return a
CircuitOp
equivalent to e^iH for this operator H.log_i
([massive])Return a
MatrixOp
equivalent to log(H)/i for this operator H.mul
(scalar)Returns the scalar multiplication of the Operator, overloaded by
*
, including support for Terra’sParameters
, which can be bound to values later (viabind_parameters
).neg
()Return the Operator’s negation, effectively just multiplying by 1.0, overloaded by

.permute
(permutation)Permutes the sequence of Pauli matrices.
power
(exponent)Return Operator composed with self multiple times, overloaded by
**
.Return a set of strings describing the primitives contained in the Operator.
reduce
()Try collapsing the Operator structure, usually after some type of conversion, e.g.
tensor
(other)Return tensor product between self and other, overloaded by
^
.tensorpower
(other)Return tensor product with self multiple times, overloaded by
^
.Returns a
QuantumCircuit
equivalent to this Operator.Returns a
CircuitOp
equivalent to this Operator.Returns an
Instruction
equivalent to this Operator.to_matrix
([massive])Return NumPy representation of the Operator.
to_matrix_op
([massive])Returns a
MatrixOp
equivalent to this Operator.to_pauli_op
([massive])Returns a sum of
PauliOp
s equivalent to this Operator.Returns SciPy sparse matrix representation of the Operator.
Attributes
INDENTATION
The scalar coefficient multiplying the Operator.
Return the unique instance id.
The number of qubits over which the Operator is defined.
Return a set of Parameter objects contained in the Operator.
The primitive defining the underlying function of the Operator.
Return operator settings.

add
(other)[source]¶ Return Operator addition of self and other, overloaded by
+
. Parameters
other (
OperatorBase
) – AnOperatorBase
with the same number of qubits as self, and in the same ‘Operator’, ‘State function’, or ‘Measurement’ category as self (i.e. the same type of underlying function). Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the sum of self and other.

adjoint
()[source]¶ Return a new Operator equal to the Operator’s adjoint (conjugate transpose), overloaded by
~
. For StateFns, this also turns the StateFn into a measurement. Return type
PauliOp
 Returns
An
OperatorBase
equivalent to the adjoint of self.

assign_parameters
(param_dict)¶ Binds scalar values to any Terra
Parameters
in the coefficients or primitives of the Operator, or substitutes oneParameter
for another. This method differs from Terra’sassign_parameters
in that it also supports lists of values to assign for a giveParameter
, in which case self will be copied for each parameterization in the binding list(s), and all the copies will be returned in anOpList
. If lists of parameterizations are used, everyParameter
in the param_dict must have the same length list of parameterizations. Parameters
param_dict (
dict
) – The dictionary ofParameters
to replace, and values or lists of values by which to replace them. Return type
OperatorBase
 Returns
The
OperatorBase
with theParameters
in self replaced by the values orParameters
in param_dict. If param_dict contains parameterization lists, thisOperatorBase
is anOpList
.

bind_parameters
(param_dict)¶ Same as assign_parameters, but maintained for consistency with QuantumCircuit in Terra (which has both assign_parameters and bind_parameters).
 Return type
OperatorBase

property
coeff
¶ The scalar coefficient multiplying the Operator.
 Return type
Union
[complex
,ParameterExpression
] Returns
The coefficient.

compose
(other, permutation=None, front=False)[source]¶ Return Operator Composition between self and other (linear algebrastyle: A@B(x) = A(B(x))), overloaded by
@
.Note: You must be conscious of Quantum Circuit vs. Linear Algebra ordering conventions. Meaning, X.compose(Y) produces an X∘Y on qubit 0, but would produce a QuantumCircuit which looks like
[Y][X]
Because Terra prints circuits with the initial state at the left side of the circuit.
 Parameters
other (
OperatorBase
) – TheOperatorBase
with which to compose self.permutation (
Optional
[List
[int
]]) –List[int]
which defines permutation on other operator.front (
bool
) – If front==True, returnother.compose(self)
.
 Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the function composition of self and other.

copy
()¶ Return a deep copy of the Operator.
 Return type
OperatorBase

equals
(other)[source]¶ Evaluate Equality between Operators, overloaded by
==
. Only returns True if self and other are of the same representation (e.g. a DictStateFn and CircuitStateFn will never be equal, even if their vector representations are equal), their underlying primitives are equal (this means for ListOps, OperatorStateFns, or EvolvedOps the equality is evaluated recursively downwards), and their coefficients are equal. Parameters
other (
OperatorBase
) – TheOperatorBase
to compare to self. Return type
bool
 Returns
A bool equal to the equality of self and other.

eval
(front=None)[source]¶ Evaluate the Operator’s underlying function, either on a binary string or another Operator. A square binary Operator can be defined as a function taking a binary function to another binary function. This method returns the value of that function for a given StateFn or binary string. For example,
op.eval('0110').eval('1110')
can be seen as querying the Operator’s matrix representation by row 6 and column 14, and will return the complex value at those “indices.” Similarly for a StateFn,op.eval('1011')
will return the complex value at row 11 of the vector representation of the StateFn, as all StateFns are defined to be evaluated from Zero implicitly (i.e. it is as if.eval('0000')
is already called implicitly to always “indexing” from column 0).If
front
is None, the matrixrepresentation of the operator is returned. Parameters
front (
Union
[str
,Dict
[str
,complex
],ndarray
,OperatorBase
,Statevector
,None
]) – The bitstring, dict of bitstrings (with values being coefficients), or StateFn to evaluated by the Operator’s underlying function, or None. Return type
Union
[OperatorBase
,complex
] Returns
The output of the Operator’s evaluation function. If self is a
StateFn
, the result is a float or complex. If self is an Operator (PrimitiveOp, ComposedOp, SummedOp, EvolvedOp,
etc.), the result is a StateFn. Iffront
is None, the matrixrepresentation of the operator is returned, which is aMatrixOp
for the operators and aVectorStateFn
for statefunctions. If either self or front contain properListOps
(not ListOp subclasses), the result is an ndimensional list of complex or StateFn results, resulting from the recursive evaluation by each OperatorBase in the ListOps.

exp_i
()[source]¶ Return a
CircuitOp
equivalent to e^iH for this operator H. Return type
OperatorBase

property
instance_id
¶ Return the unique instance id.
 Return type
int

log_i
(massive=False)¶ Return a
MatrixOp
equivalent to log(H)/i for this operator H. This function is the effective inverse of exp_i, equivalent to finding the Hermitian Operator which produces self when exponentiated. Return type
OperatorBase

mul
(scalar)¶ Returns the scalar multiplication of the Operator, overloaded by
*
, including support for Terra’sParameters
, which can be bound to values later (viabind_parameters
). Parameters
scalar (
Union
[complex
,ParameterExpression
]) – The real or complex scalar by which to multiply the Operator, or theParameterExpression
to serve as a placeholder for a scalar factor. Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to product of self and scalar.

neg
()¶ Return the Operator’s negation, effectively just multiplying by 1.0, overloaded by

. Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the negation of self.

property
num_qubits
¶ The number of qubits over which the Operator is defined. If
op.num_qubits == 5
, thenop.eval('1' * 5)
will be valid, butop.eval('11')
will not. Return type
int
 Returns
The number of qubits accepted by the Operator’s underlying function.

property
parameters
¶ Return a set of Parameter objects contained in the Operator.

permute
(permutation)[source]¶ Permutes the sequence of Pauli matrices.
 Parameters
permutation (
List
[int
]) – A list defining where each Pauli should be permuted. The Pauli at index j of the primitive should be permuted to position permutation[j]. Return type
PauliOp
 Returns
A new PauliOp representing the permuted operator. For operator (X ^ Y ^ Z) and indices=[1,2,4], it returns (X ^ I ^ Y ^ Z ^ I).
 Raises
OpflowError – if indices do not define a new index for each qubit.

power
(exponent)¶ Return Operator composed with self multiple times, overloaded by
**
.

property
primitive
¶ The primitive defining the underlying function of the Operator.
 Return type
Union
[QuantumCircuit
,Operator
,Pauli
,SparsePauliOp
,OperatorBase
] Returns
The primitive object.

primitive_strings
()[source]¶ Return a set of strings describing the primitives contained in the Operator. For example,
{'QuantumCircuit', 'Pauli'}
. For hierarchical Operators, such asListOps
, this can help illuminate the primitives represented in the various recursive levels, and therefore which conversions can be applied. Return type
Set
[str
] Returns
A set of strings describing the primitives contained within the Operator.

reduce
()¶ Try collapsing the Operator structure, usually after some type of conversion, e.g. trying to add Operators in a SummedOp or delete needless IGates in a CircuitOp. If no reduction is available, just returns self.
 Return type
OperatorBase
 Returns
The reduced
OperatorBase
.

property
settings
¶ Return operator settings.
 Return type
Dict

tensor
(other)[source]¶ Return tensor product between self and other, overloaded by
^
. Note: You must be conscious of Qiskit’s bigendian bit printing convention. Meaning, X.tensor(Y) produces an X on qubit 0 and an Y on qubit 1, or X⨂Y, but would produce a QuantumCircuit which looks like[Y] [X]
Because Terra prints circuits and results with qubit 0 at the end of the string or circuit.
 Parameters
other (
OperatorBase
) – TheOperatorBase
to tensor product with self. Return type
OperatorBase
 Returns
An
OperatorBase
equivalent to the tensor product of self and other.

tensorpower
(other)¶ Return tensor product with self multiple times, overloaded by
^
. Parameters
other (
int
) – The int number of times to tensor product self with itself viatensorpower
. Return type
Union
[OperatorBase
,int
] Returns
An
OperatorBase
equivalent to the tensorpower of self by other.

to_circuit
()[source]¶ Returns a
QuantumCircuit
equivalent to this Operator. Return type
QuantumCircuit

to_circuit_op
()¶ Returns a
CircuitOp
equivalent to this Operator. Return type
OperatorBase

to_instruction
()[source]¶ Returns an
Instruction
equivalent to this Operator. Return type
Instruction

to_matrix
(massive=False)[source]¶ Return NumPy representation of the Operator. Represents the evaluation of the Operator’s underlying function on every combination of basis binary strings. Warn if more than 16 qubits to force having to set
massive=True
if such a large vector is desired. Return type
ndarray
 Returns
The NumPy
ndarray
equivalent to this Operator.

to_matrix_op
(massive=False)¶ Returns a
MatrixOp
equivalent to this Operator. Return type
OperatorBase