Causal structures and the classification of higher order quantum computations

Understand

Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits.

• The class of quantum transformations can be extended by including transformations on quantum operations, and transformations thereof, and so on up to the construction of a potentially infinite hierarchy of transformations.
• In the last decade, a sub-hierarchy, known as quantum combs, was exhaustively studied, and characterised as the most general class of transformations that can be achieved by quantum circuits with open slots hosting variable input elements, to form a complete output quantum circuit.
• The theory of quantum combs proved to be successful for the optimisation of information processing tasks otherwise untreatable.