title: Experimental superposition of orders of quantum gates.
abstract: 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.
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Lorenzo M
authors.initials: LM
authors.lastname: Procopio
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Amir
authors.initials: A
authors.lastname: Moqanaki
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.|Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria.
authors.forename: Mateus
authors.initials: M
authors.lastname: Araújo
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.|Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria.
authors.forename: Fabio
authors.initials: F
authors.lastname: Costa
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Irati
authors.initials: I
authors.lastname: Alonso Calafell
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Emma G
authors.initials: EG
authors.lastname: Dowd
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Deny R
authors.identifier: http://orcid.org/0000-0002-4788-7548
authors.initials: DR
authors.lastname: Hamel
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Lee A
authors.initials: LA
authors.lastname: Rozema
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.|Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria.
authors.forename: Časlav
authors.initials: Č
authors.lastname: Brukner
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.
authors.forename: Philip
authors.initials: P
authors.lastname: Walther