Berlin 2014 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 59: Quantum information: Quantum computers and communication I
Q 59.4: Talk
Friday, March 21, 2014, 11:15–11:30, DO26 207
Quantum circuits cannot control unknown operations — Mateus Araújo1,2, •Adrien Feix1,2, Fabio Costa1,2, and Časlav Brukner1,2 — 1Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria — 2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
One of the essential building blocks of classical computer programs is the ``if'' clause, which executes a subroutine depending on the value of a control variable. Several quantum algorithms rely on a similar possibility of applying a quantum operation conditioned on the state of a control system.
We prove a no-go theorem, showing that no quantum circuit can conditionally apply a completely unknown unitary. Yet, such a quantum control has been experimentally implemented in interferometric setups. We explain this discrepancy by the fact that every physical realization of a unitary acts nontrivially only on a subspace of a larger Hilbert space, effectively providing some information about the operation.
We argue that the quantum circuit model should be extended for this type of very natural extension. Furthermore, our results open up the possibility to greatly simplify the implementation of quantum algorithms.