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SUMMARY:Routed quantum circuits - Hlér Kristjánsson\, Department of Comp
 uter Science\, University of Oxford
DTSTART:20211125T141500Z
DTEND:20211125T151500Z
UID:TALK165244@talks.cam.ac.uk
CONTACT:Damian Pitalua-Garcia
DESCRIPTION:We argue that the quantum-theoretical structures studied in se
 veral recent lines of research cannot be adequately described within the s
 tandard framework of quantum circuits. This is in particular the case when
 ever the combination of subsystems is described by a nontrivial blend of d
 irect sums and tensor products of Hilbert spaces. We therefore propose an 
 extension to the framework of quantum circuits\, given by routed linear ma
 ps and routed quantum circuits. We prove that this new framework allows fo
 r a consistent and intuitive diagrammatic representation in terms of circu
 it diagrams\, applicable to both pure and mixed quantum theory\, and exemp
 lify its use in several situations\, including the superposition of quantu
 m channels and the causal decompositions of unitaries. We show that our fr
 amework encompasses the 'extended circuit diagrams' of Lorenz and Barrett 
 [arXiv:2001.07774 (2020)]\, which we derive as a special case\, endowing t
 hem with a sound semantics.
LOCATION:MR2 Centre for Mathematical Sciences
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