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# ComposedOp

class `ComposedOp(oplist, coeff=1.0, abelian=False)`

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

Parameters

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

## Methods Defined Here

`ComposedOp.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

`ComposedOp`

Returns

An `OperatorBase` equivalent to the adjoint of self.

### compose

`ComposedOp.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.

### eval

`ComposedOp.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`, `ndarray`, `OperatorBase`, `Statevector`, `None`]) – The bitstring, dict of bitstrings (with values being coefficients), or StateFn to evaluated by the Operator’s underlying function.

Return type

`Union`[`OperatorBase`, `complex`]

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.

### non_distributive_reduce

`ComposedOp.non_distributive_reduce()`

Reduce without attempting to expand all distributive compositions.

Return type

`OperatorBase`

Returns

The reduced Operator.

### reduce

`ComposedOp.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`.

### to_circuit

`ComposedOp.to_circuit()`

Returns the quantum circuit, representing the composed operator.

Return type

`QuantumCircuit`

Returns

The circuit representation of the composed operator.

Raises

OpflowError – for operators where a single underlying circuit can not be obtained.

### to_matrix

`ComposedOp.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.

## Attributes

### INDENTATION

Default value: `'  '`

### 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.

### coeff

The scalar coefficient multiplying the Operator.

Return type

`Union`[`complex`, `ParameterExpression`]

Returns

The coefficient.

### coeffs

Return a list of the coefficients of the operators listed. Raises exception for nested Listops.

Return type

`List`[`Union`[`complex`, `ParameterExpression`]]

### 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.

### distributive

Return type

`bool`

The gradient of `combo_fn`.

Return type

`Optional`[`Callable`]

### instance_id

Return the unique instance id.

Return type

`int`

Return type

`int`

### oplist

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

Return type

`List`[`OperatorBase`]

Returns

The Operators defining the ListOp

Return settings.

Return type

`Dict`