# qiskit.opflow.list_ops.SummedOp¶

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

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.

Parameter
• oplist (List[OperatorBase]) – The Operators being summed.

• coeff (Union[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)[Quellcode]
Parameter
• oplist (List[OperatorBase]) – The Operators being summed.

• coeff (Union[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 +. 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). 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 @. Return a deep copy of the Operator. ListOp default combo function i.e. lambda x: x. 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. 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). 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 **. Return a set of strings describing the primitives contained in the Operator. 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 ^. Returns the quantum circuit, representing the SummedOp. Returns an equivalent Operator composed of only QuantumCircuit-based primitives, such as CircuitOp and CircuitStateFn. 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. 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. instance_id Return the unique instance id. 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. settings Return settings.
property abelian

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

Rückgabetyp

bool

Rückgabe

A bool indicating whether the oplist is Abelian.

add(other)[Quellcode]

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

Bemerkung

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

Parameter

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).

Rückgabetyp

SummedOp

Rückgabe

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.

Rückgabetyp

ListOp

Rückgabe

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.

Parameter

param_dict (dict) – The dictionary of Parameters to replace, and values or lists of values by which to replace them.

Rückgabetyp

OperatorBase

Rückgabe

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).

Rückgabetyp

OperatorBase

property coeff

The scalar coefficient multiplying the Operator.

Rückgabetyp

Union[complex, ParameterExpression]

Rückgabe

The coefficient.

collapse_summands()[Quellcode]

Return Operator by simplifying duplicate operators.

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

Rückgabetyp

SummedOp

Rückgabe

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.

Rückgabetyp

Callable

Rückgabe

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.

Parameter
• 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).

Rückgabetyp

OperatorBase

Rückgabe

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

copy()

Return a deep copy of the Operator.

Rückgabetyp

OperatorBase

static default_combo_fn(x)

ListOp default combo function i.e. lambda x: x

Rückgabetyp

Any

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.

Rückgabetyp

bool

Rückgabe

A bool indicating whether the ListOp is distributive under composition.

equals(other)[Quellcode]

Check if other is equal to self.

Bemerkung

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.

Parameter

other (OperatorBase) – The other operator to check for equality.

Rückgabetyp

bool

Rückgabe

True, if other and self are equal, otherwise False.

Examples

>>> from qiskit.opflow 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.

Parameter

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.

Rückgabetyp

Union[OperatorBase, complex]

Rückgabe

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.

Verursacht
• 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).

Rückgabetyp

OperatorBase

property grad_combo_fn

The gradient of combo_fn.

Rückgabetyp

Optional[Callable]

property instance_id

Return the unique instance id.

Rückgabetyp

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

Rückgabetyp

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).

Parameter

scalar (Union[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.

Rückgabetyp

ListOp

Rückgabe

An OperatorBase equivalent to product of self and scalar.

neg()

Return the Operator’s negation, effectively just multiplying by -1.0, overloaded by -.

Rückgabetyp

OperatorBase

Rückgabe

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.

Rückgabetyp

int

Rückgabe

The number of qubits accepted by the Operator’s underlying function.

property oplist

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

Rückgabetyp

List[OperatorBase]

Rückgabe

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.

Parameter

permutation (List[int]) – A list defining where each qubit should be permuted. The qubit at index j should be permuted to position permutation[j].

Rückgabetyp

OperatorBase

Rückgabe

A new ListOp representing the permuted operator.

Verursacht

OpflowError – if indices do not define a new index for each qubit.

power(exponent)

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

Rückgabetyp

OperatorBase

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.

Rückgabetyp

Set[str]

Rückgabe

A set of strings describing the primitives contained within the Operator.

reduce()[Quellcode]

Try collapsing list or trees of sums.

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

Rückgabetyp

OperatorBase

Rückgabe

A collapsed version of self, if possible.

property settings

Return settings.

Rückgabetyp

Dict

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.

Parameter

other (OperatorBase) – The OperatorBase to tensor product with self.

Rückgabetyp

OperatorBase

Rückgabe

An OperatorBase equivalent to the tensor product of self and other.

tensorpower(other)

Return tensor product with self multiple times, overloaded by ^.

Parameter

other (int) – The int number of times to tensor product self with itself via tensorpower.

Rückgabetyp

Union[OperatorBase, int]

Rückgabe

An OperatorBase equivalent to the tensorpower of self by other.

to_circuit()[Quellcode]

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 parameterized PrimitiveOps (in that case, OpflowError 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.

Rückgabetyp

QuantumCircuit

Rückgabe

The circuit representation of the summed operator.

Verursacht
• OpflowError – if SummedOp can not be converted to MatrixOp (e.g. SummedOp is composed of

• parameterized PrimitiveOps)

to_circuit_op()

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

Rückgabetyp

OperatorBase

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.

Rückgabetyp

ndarray

Rückgabe

The NumPy ndarray equivalent to this Operator.

to_matrix_op(massive=False)[Quellcode]

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

Rückgabetyp

SummedOp

to_pauli_op(massive=False)[Quellcode]

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

Rückgabetyp

SummedOp

to_spmatrix()

Returns SciPy sparse matrix representation of the Operator.

Rückgabetyp

Union[spmatrix, List[spmatrix]]

Rückgabe

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.

Parameter
• convert_fn (Callable) – The function to apply to the internal OperatorBase.

• coeff (Union[complex, ParameterExpression, None]) – A coefficient to multiply by after applying convert_fn. If it is None, self.coeff is used instead.

Rückgabetyp

ListOp

Rückgabe

The converted ListOp.