qiskit.aqua.operators.list_ops.SummedOp¶

class SummedOp(oplist, coeff=1.0, abelian=False)[source]¶

A class for lazily representing sums of Operators. Often Operators cannot be efficiently added to one another, but may be manipulated further so that they can be later. This class holds logic to indicate that the Operators in oplist are meant to be added together, and therefore if they reach a point in which they can be, such as after evaluation or conversion to matrices, they can be reduced by addition.

Parameters

oplist (List[OperatorBase]) – The Operators being summed.
coeff (Union[int, float, complex, ParameterExpression]) – A coefficient multiplying the operator
abelian (bool) – Indicates whether the Operators in oplist are known to mutually commute.

__init__(oplist, coeff=1.0, abelian=False)[source]¶

Parameters

oplist (List[OperatorBase]) – The Operators being summed.
coeff (Union[int, float, complex, ParameterExpression]) – A coefficient multiplying the operator
abelian (bool) – Indicates whether the Operators in oplist are known to mutually commute.

Methods

`__init__`(oplist[, coeff, abelian])	type oplist `List`[`OperatorBase`]
`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 one `Parameter` 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).
`collapse_summands`()	Return Operator by simplifying duplicate operators.
`compose`(other[, permutation, front])	Return Operator Composition between self and other (linear algebra-style: A@B(x) = A(B(x))), overloaded by `@`.
`equals`(other)	Check if other is equal to self.
`eval`([front])	Evaluate the Operator’s underlying function, either on a binary string or another Operator.
`exp_i`()	Return an `OperatorBase` equivalent to an exponentiation of self * -i, e^(-i*op).
`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’s `Parameters`, which can be bound to values later (via `bind_parameters`).
`neg`()	Return the Operator’s negation, effectively just multiplying by -1.0, overloaded by `-`.
`permute`(permutation)	Permute the qubits of the operator.
`power`(exponent)	Return Operator composed with self multiple times, overloaded by `**`.
`primitive_strings`()	Return a set of strings describing the primitives contained in the Operator.
`print_details`()	Print out the operator in details.
`reduce`()	Try collapsing list or trees of sums.
`tensor`(other)	Return tensor product between self and other, overloaded by `^`.
`tensorpower`(other)	Return tensor product with self multiple times, overloaded by `^`.
`to_circuit`()	Returns the quantum circuit, representing the SummedOp.
`to_circuit_op`()	Returns an equivalent Operator composed of only QuantumCircuit-based primitives, such as `CircuitOp` and `CircuitStateFn`.
`to_legacy_op`([massive])	Attempt to return the Legacy Operator representation of the Operator.
`to_matrix`([massive])	Return NumPy representation of the Operator.
`to_matrix_op`([massive])	Returns an equivalent Operator composed of only NumPy-based primitives, such as `MatrixOp` and `VectorStateFn`.
`to_pauli_op`([massive])	Returns an equivalent Operator composed of only Pauli-based primitives, such as `PauliOp`.
`to_spmatrix`()	Returns SciPy sparse matrix representation of the Operator.
`traverse`(convert_fn[, coeff])	Apply the convert_fn to each node in the oplist.

Attributes

`INDENTATION`
`abelian`	Whether the Operators in `oplist` are known to commute with one another.
`coeff`	The scalar coefficient multiplying the Operator.
`combo_fn`	The function defining how to combine `oplist` (or Numbers, or NumPy arrays) to produce the Operator’s underlying function.
`distributive`	Indicates whether the ListOp or subclass is distributive under composition.
`grad_combo_fn`	The gradient of `combo_fn`.
`num_qubits`	The number of qubits over which the Operator is defined.
`oplist`	The list of `OperatorBases` defining the underlying function of this Operator.
`parameters`	Return a set of Parameter objects contained in the Operator.

property abelian¶

Whether the Operators in oplist are known to commute with one another.

Return type: bool
Returns: A bool indicating whether the oplist is Abelian.

add(other)[source]¶

Return Operator addition of self and other, overloaded by +.

Note

This appends other to self.oplist without checking other is already included or not. If you want to simplify them, please use simplify().

Parameters: other (OperatorBase) – An OperatorBase 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: A SummedOp equivalent to the sum of self and other.

adjoint()¶

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: OperatorBase
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 one Parameter for another. This method differs from Terra’s assign_parameters in that it also supports lists of values to assign for a give Parameter, in which case self will be copied for each parameterization in the binding list(s), and all the copies will be returned in an OpList. If lists of parameterizations are used, every Parameter in the param_dict must have the same length list of parameterizations.

Parameters: param_dict (dict) – The dictionary of Parameters to replace, and values or lists of values by which to replace them.
Return type: OperatorBase
Returns: The OperatorBase with the Parameters in self replaced by the values or Parameters in param_dict. If param_dict contains parameterization lists, this OperatorBase is an OpList.

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[int, float, complex, ParameterExpression]
Returns: The coefficient.

collapse_summands()[source]¶

Return Operator by simplifying duplicate operators.

E.g., SummedOp([2 * X ^ Y, X ^ Y]).collapse_summands() -> SummedOp([3 * X ^ Y]).

Return type: SummedOp
Returns: A simplified SummedOp equivalent to self.

property combo_fn¶

The function defining how to combine oplist (or Numbers, or NumPy arrays) to produce the Operator’s underlying function. For example, SummedOp’s combination function is to add all of the Operators in oplist.

Return type: Callable
Returns: The combination function.

compose(other, permutation=None, front=False)¶

Return Operator Composition between self and other (linear algebra-style: 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) – The OperatorBase with which to compose self.
permutation (Optional[List[int]]) – List[int] which defines permutation on other operator.
front (bool) – If front==True, return other.compose(self).

Return type

OperatorBase

Returns

An OperatorBase equivalent to the function composition of self and other.

property distributive¶

Indicates whether the ListOp or subclass is distributive under composition. ListOp and SummedOp are, meaning that (opv @ op) = (opv[0] @ op + opv[1] @ op) (using plus for SummedOp, list for ListOp, etc.), while ComposedOp and TensoredOp do not behave this way.

Return type: bool
Returns: A bool indicating whether the ListOp is distributive under composition.

equals(other)[source]¶

Check if other is equal to self.

Note

This is not a mathematical check for equality. If self and other implement the same operation but differ in the representation (e.g. different type of summands) equals will evaluate to False.

Parameters: other (OperatorBase) – The other operator to check for equality.
Return type: bool
Returns: True, if other and self are equal, otherwise False.

Examples

>>> from qiskit.aqua.operators import X, Z
>>> 2 * X == X + X
True
>>> X + Z == Z + X
True

eval(front=None)¶

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).

ListOp’s eval recursively evaluates each Operator in oplist, and combines the results using the recombination function combo_fn.

Parameters

front (Union[str, Dict[str, complex], OperatorBase, None]) – The bitstring, dict of bitstrings (with values being coefficients), or StateFn to evaluated by the Operator’s underlying function.

Return type

Union[OperatorBase, float, complex, list]

Returns

The output of the oplist Operators’ evaluation function, combined with the combo_fn. If either self or front contain proper ListOps (not ListOp subclasses), the result is an n-dimensional list of complex or StateFn results, resulting from the recursive evaluation by each OperatorBase in the ListOps.

Raises

NotImplementedError – Raised if called for a subclass which is not distributive.
TypeError – Operators with mixed hierarchies, such as a ListOp containing both PrimitiveOps and ListOps, are not supported.
NotImplementedError – Attempting to call ListOp’s eval from a non-distributive subclass.

exp_i()¶

Return an OperatorBase equivalent to an exponentiation of self * -i, e^(-i*op).

Return type: OperatorBase

property grad_combo_fn¶

The gradient of combo_fn.

Return type: Optional[Callable]

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. For proper ListOps, applies log_i to all ops in oplist.

Return type: OperatorBase

mul(scalar)¶

Returns the scalar multiplication of the Operator, overloaded by *, including support for Terra’s Parameters, which can be bound to values later (via bind_parameters).

Parameters: scalar (Union[int, float, complex, ParameterExpression]) – The real or complex scalar by which to multiply the Operator, or the ParameterExpression 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, then op.eval('1' * 5) will be valid, but op.eval('11') will not.

Return type: int
Returns: The number of qubits accepted by the Operator’s underlying function.

property oplist¶

The list of OperatorBases defining the underlying function of this Operator.

Return type: List[OperatorBase]
Returns: The Operators defining the ListOp

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

permute(permutation)¶

Permute the qubits of the operator.

Parameters: permutation (List[int]) – A list defining where each qubit should be permuted. The qubit at index j should be permuted to position permutation[j].
Return type: ListOp
Returns: A new ListOp representing the permuted operator.
Raises: AquaError – if indices do not define a new index for each qubit.

power(exponent)¶

Return Operator composed with self multiple times, overloaded by **.

Parameters: exponent (int) – The int number of times to compose self with itself.
Return type: OperatorBase
Returns: An OperatorBase equivalent to self composed with itself exponent times.

primitive_strings()¶

Return a set of strings describing the primitives contained in the Operator. For example, {'QuantumCircuit', 'Pauli'}. For hierarchical Operators, such as ListOps, 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.

print_details()[source]¶: Print out the operator in details. :returns: a formatted string describes the operator. :rtype: str

reduce()[source]¶

Try collapsing list or trees of sums.

Tries to sum up duplicate operators and reduces the operators in the sum.

Return type: OperatorBase
Returns: A collapsed version of self, if possible.

tensor(other)¶

Return tensor product between self and other, overloaded by ^. Note: You must be conscious of Qiskit’s big-endian 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) – The OperatorBase 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 via tensorpower.
Return type: Union[OperatorBase, int]
Returns: An OperatorBase equivalent to the tensorpower of self by other.

to_circuit()[source]¶

Returns the quantum circuit, representing the SummedOp. In the first step, the SummedOp is converted to MatrixOp. This is straightforward for most operators, but it is not supported for operators containing parametrized PrimitiveOps (in that case, AquaError is raised). In the next step, the MatrixOp representation of SummedOp is converted to circuit. In most cases, if the summands themselves are unitary operators, the SummedOp itself is non-unitary and can not be converted to circuit. In that case, ExtensionError is raised in the underlying modules.

Return type

QuantumCircuit

Returns

The circuit representation of the summed operator.

Raises

AquaError – if SummedOp can not be converted to MatrixOp (e.g. SummedOp is composed of
parametrized PrimitiveOps) –

to_circuit_op()¶

Returns an equivalent Operator composed of only QuantumCircuit-based primitives, such as CircuitOp and CircuitStateFn.

Return type: OperatorBase

to_legacy_op(massive=False)[source]¶

Attempt to return the Legacy Operator representation of the Operator. If self is a SummedOp of PauliOps, will attempt to convert to WeightedPauliOperator, and otherwise will simply convert to MatrixOp and then to MatrixOperator. The Legacy Operators cannot represent StateFns or proper ListOps (meaning not one of the ListOp subclasses), so an error will be thrown if this method is called on such an Operator. Also, Legacy Operators cannot represent unbound Parameter coeffs, so an error will be thrown if any are present in self.

Warn if more than 16 qubits to force having to set massive=True if such a large vector is desired.

Return type: LegacyBaseOperator
Returns: The LegacyBaseOperator representing this Operator.
Raises: TypeError – self is an Operator which cannot be represented by a LegacyBaseOperator, such as StateFn, proper (non-subclass) ListOp, or an Operator with an unbound coeff Parameter.

to_matrix(massive=False)¶

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)[source]¶

Returns an equivalent Operator composed of only NumPy-based primitives, such as MatrixOp and VectorStateFn.

Return type: OperatorBase

to_pauli_op(massive=False)¶

Returns an equivalent Operator composed of only Pauli-based primitives, such as PauliOp.

Return type: OperatorBase

to_spmatrix()¶

Returns SciPy sparse matrix representation of the Operator.

Return type: Union[spmatrix, List[spmatrix]]
Returns: CSR sparse matrix representation of the Operator, or List thereof.

traverse(convert_fn, coeff=None)¶

Apply the convert_fn to each node in the oplist.

Parameters

convert_fn (Callable) – The function to apply to the internal OperatorBase.
coeff (Union[int, float, complex, ParameterExpression, None]) – A coefficient to multiply by after applying convert_fn. If it is None, self.coeff is used instead.

Return type

OperatorBase

Returns

The converted ListOp.