Experimentally feasible computational advantage from quantum superposition of gate orders

Understand

In an ordinary quantum algorithm the gates are applied in a fixed order on the systems.

• The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state.
• It is known that this quantum-controlled ordering of gates can reduce the query complexity in deciding a property of black-box unitaries with respect to the best algorithm in which the gates are applied in a fixed order.
• However, all tasks explicitly found so far require unitaries that either act on unbounded dimensional quantum systems in the asymptotic limit (the limiting case of a large number of black-box gates) or act on qubits, but then involve only a few unitaries.