qiskit.aqua.operators.list_ops.ListOp

class ListOp(oplist, combo_fn=<function ListOp.<lambda>>, coeff=1.0, abelian=False, grad_combo_fn=None)

A Class for manipulating List Operators, and parent class to SummedOp, ComposedOp, and TensoredOp.

List Operators are classes for storing and manipulating lists of Operators, State functions, or Measurements, and include some rule or combo_fn defining how the Operator functions of the list constituents should be combined to form to cumulative Operator function of the ListOp. For example, a SummedOp has an addition-based combo_fn, so once the Operators in its list are evaluated against some bitstring to produce a list of results, we know to add up those results to produce the final result of the SummedOp’s evaluation. In theory, this combo_fn can be any function over classical complex values, but for convenience we’ve chosen for them to be defined over NumPy arrays and values. This way, large numbers of evaluations, such as after calling to_matrix on the list constituents, can be efficiently combined. While the combination function is defined over classical values, it should be understood as the operation by which each Operators’ underlying function is combined to form the underlying Operator function of the ListOp. In this way, the ListOps are the basis for constructing large and sophisticated Operators, State Functions, and Measurements in Aqua.

The base ListOp class is particularly interesting, as its combo_fn is “the identity list Operation”. Meaning, if we understand the combo_fn as a function from a list of complex values to some output, one such function is returning the list as-is. This is powerful for constructing compact hierarchical Operators which return many measurements in multiple dimensional lists.

Parameters

• oplist (List[OperatorBase]) – The list of OperatorBases defining this Operator’s underlying function.

• combo_fn (callable) – The recombination function to combine classical results of the oplist Operators’ eval functions (e.g. sum).

• coeff (Union[int, float, complex, ParameterExpression]) – A coefficient multiplying the operator

• abelian (bool) – Indicates whether the Operators in oplist are known to mutually commute.

• grad_combo_fn (Optional[Callable]) – The gradient of recombination function. If None, the gradient will be computed automatically.

• that the default "recombination function" lambda above is essentially the (Note) –

• - it accepts the list of values (identity) –

• returns them in a list. (and) –

__init__(oplist, combo_fn=<function ListOp.<lambda>>, coeff=1.0, abelian=False, grad_combo_fn=None)

Parameters

• oplist (List[OperatorBase]) – The list of OperatorBases defining this Operator’s underlying function.

• combo_fn (callable) – The recombination function to combine classical results of the oplist Operators’ eval functions (e.g. sum).

• coeff (Union[int, float, complex, ParameterExpression]) – A coefficient multiplying the operator

• abelian (bool) – Indicates whether the Operators in oplist are known to mutually commute.

• grad_combo_fn (Optional[Callable]) – The gradient of recombination function. If None, the gradient will be computed automatically.

• that the default "recombination function" lambda above is essentially the (Note) –

• - it accepts the list of values (identity) –

• returns them in a list. (and) –

Methods

__init__(oplist[, combo_fn, 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).
compose(other[, permutation, front])	Return Operator Composition between self and other (linear algebra-style: A@B(x) = A(B(x))), overloaded by @.
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 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.
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 ^.
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)

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

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

An OperatorBase 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.

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)

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) – The OperatorBase to compare to self.

Return type

bool

Returns

A bool equal to the equality of self and other.

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.

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.

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_op()

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

Return type

OperatorBase

to_legacy_op(massive=False)

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)

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.