Develop a full theory of the physical implementation of control

Develop a full account of the physical implementation of control in controlled PROPs, including the possibility of controlling unknown quantum operations within the standard quantum circuit formalism.

Background

The paper develops controlled PROPs as an abstract diagrammatic formalism in which control is treated as a constructor, independently of how controlled operations are physically realized. The authors note that standard quantum circuits face a no-go theorem concerning the control of unknown operations, although practical implementations may provide additional information about the operation and thereby evade the theorem.

The authors leave the full development of the physical-implementation question unresolved. This is relevant because the controlled quantum-circuit language introduced in the paper can represent controlled unknown unitaries at the circuit level, while the physical realization of that capability is not developed.