Quantum Blindness: While quantum computers offer speed advantages over their classical counterparts, the technological challenges facing their eventual realization suggest that they will need to be located in specialized facilities. Thus, interaction would then need to be on a quantum client:quantum server basis.Barzet al.(p.303; see the Perspective byVedral) implemented a proof-of-principle protocol that illustrates complete security in such a setup—for both the client and the server. In this blind quantum computing protocol, the client maintains the security of their data and the specifics of the calculation they want to perform, and the server cannot access the data or calculation of the client.

Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to ‘superimpose different operations’. Furthermore, it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task—determining if two gates commute or anti-commute—with fewer gate uses than any known quantum algorithm. Here we experimentally demonstrate this advantage, in a photonic context, using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders by using additional degrees of freedom of the photons encoding our qubits. The new resource we exploit can be interpreted as a superposition of causal orders, and could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer.