Quantum circuits cannot control unknown operations

Araujo, Mateus, Feix, Adrien, Costa, Fabio and Brukner, Caslav (2014) Quantum circuits cannot control unknown operations. New Journal of Physics, 16 . doi:10.1088/1367-2630/16/9/093026

Author Araujo, Mateus
Feix, Adrien
Costa, Fabio
Brukner, Caslav
Title Quantum circuits cannot control unknown operations
Journal name New Journal of Physics   Check publisher's open access policy
ISSN 1367-2630
Publication date 2014-09-22
Year available 2014
Sub-type Article (original research)
DOI 10.1088/1367-2630/16/9/093026
Open Access Status DOI
Volume 16
Total pages 7
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
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.
Keyword Quantum algorithms
Quantum computation
Quantum information
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 13 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 14 times in Scopus Article | Citations
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