Functors are factories that allow to access particular specialization implementations of a callable. Q# currently supports two functors; the
Adjoint and the
Controlled, both of which can be applied to operations that provide the necessary specialization(s).
Adjoint functors commute; if
ApplyUnitary is an operation that supports both functors, then there is no difference between
Controlled Adjoint ApplyUnitary and
Adjoint Controlled ApplyUnitary.
Both have the same type and upon invocation execute the implementation defined for the
controlled adjoint specialization.
If the operation
ApplyUnitary defines a unitary transformation U of the quantum state,
Adjoint ApplyUnitary accesses the implementation of U†. The
Adjoint functor is its own inverse, since (U†)† = U by definition; i.e.
Adjoint Adjoint ApplyUnitary is the same as
Adjoint ApplyUnitary is an operation of the same type as
ApplyUnitary; it has the same argument and return type and supports the same functors. Like any operation, it can be invoked with an argument of suitable type. The following expression will apply the adjoint specialization of
ApplyUnitary to an argument
For an operation
ApplyUnitary that defines a unitary transformation U of the quantum state,
Controlled ApplyUnitary accesses the implementation that applies U conditional on all qubits in an array of control qubits being in the |1⟩ state.
Controlled ApplyUnitary is an operation with the same return type and operation characteristics as
ApplyUnitary, meaning it supports the same functors.
It takes an argument of type
(Qubit, <TIn>), where
<TIn> should be replaced with the argument type of
ApplyUnitary, taking singleton tuple equivalence into account.
|Operation||Argument Type||Controlled Argument Type|
cs contains an array of qubits,
q2 are two qubits, and the operation
SWAP is as defined here, then the following expression exchanges the state of
q2 if all qubits in
cs are in the |1⟩ state:
Controlled SWAP(cs, (q1, q2))
Conditionally applying an operation based on the control qubits being in another state than a zero-state may be achieved by applying the appropriate adjointable transformation to the control qubits before invocation, and applying is inverses after. Conditioning the transformation on all control qubits being in the |0⟩ state, for example, can be achieved by applying the
Xoperation before and after. This can be conveniently expressed using a conjugation. Nonetheless, the verbosity of such a construct may merit additional support for a more compact syntax in the future.