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Quantum circuits cannot control unknown operations

Autor(en)
Mateus Araujo, Adrien Feix, Fabio Costa, Caslav Brukner
Abstrakt

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. Similarly, several quantum algorithms rely on applying a unitary operation conditioned on the state of a control system. Here we show that this control cannot be performed by a quantum circuit if the unitary is completely unknown. The task remains impossible even if we allow the control to be done modulo a global phase. However, this no-go theorem does not prevent implementing quantum control of unknown unitaries in practice, as any physical implementation of an unknown unitary provides additional information that makes the control possible. We then argue that one should extend the quantum circuit formalism to capture this possibility in a straightforward way. This is done by allowing unknown unitaries to be applied to subspaces and not only to subsystems.

Organisation(en)
Quantenoptik, Quantennanophysik und Quanteninformation
Externe Organisation(en)
Österreichische Akademie der Wissenschaften (ÖAW)
Journal
New Journal of Physics
Band
16
Anzahl der Seiten
7
ISSN
1367-2630
DOI
https://doi.org/10.1088/1367-2630/16/9/093026
Publikationsdatum
09-2014
Peer-reviewed
Ja
ÖFOS 2012
103025 Quantenmechanik
Schlagwörter
ASJC Scopus Sachgebiete
Allgemeine Physik und Astronomie
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/66a00282-556d-436e-8506-07e27e55f6f5