Reassessing the computational advantage of quantum-controlled ordering of gates

Understand

Research on indefinite causal structures is a rapidly evolving field that has a potential not only to make a radical revision of the classical understanding of space-time but also to achieve enhanced functionalities of quantum information processing.

• For example, it is known that indefinite causal structures provide exponential advantage in communication complexity when compared to causal protocols.
• In quantum computation, such structures can decide whether two unitary gates commute or anticommute with a single call to each gate, which is impossible with conventional (causal) quantum algorithms.
• A generalization of this effect to $n$ unitary gates, originally introduced in M.