Quantum circuits cannot control unknown operations

Author(s)
Mateus Araujo, Adrien Feix, Fabio Costa, Caslav Brukner
Abstract

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(s)
Quantum Optics, Quantum Nanophysics and Quantum Information
External organisation(s)
Österreichische Akademie der Wissenschaften (ÖAW)
Journal
New Journal of Physics
Volume
16
No. of pages
7
ISSN
1367-2630
DOI
https://doi.org/10.1088/1367-2630/16/9/093026
Publication date
09-2014
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics
Keywords
ASJC Scopus subject areas
General Physics and Astronomy
Portal url
https://ucrisportal.univie.ac.at/en/publications/66a00282-556d-436e-8506-07e27e55f6f5