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