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
- Physics and Astronomy(all)
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/quantum-circuits-cannot-control-unknown-operations(66a00282-556d-436e-8506-07e27e55f6f5).html