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CATEGORIES:CQIF Seminar
SUMMARY:Completeness results for graphical quantum process
languages - Miriam Backens (University of Bristol
)
DTSTART;TZID=Europe/London:20151029T141500
DTEND;TZID=Europe/London:20151029T151500
UID:TALK61130AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61130
DESCRIPTION:From Feynman diagrams via Penrose graphical notati
on to quantum circuits\, graphical languages are w
idely used in quantum theory and other areas of th
eoretical physics. The category-theoretical approa
ch to quantum mechanics yields a new set of graphi
cal languages\, which allow rigorous and intuitive
pictorial reasoning about quantum systems and pro
cesses. One such language is the ZX-calculus\, whi
ch is built up of elements corresponding to maps i
n the computational and the Hadamard basis. We sho
w that this graphical language is complete for sta
bilizer quantum mechanics and for the single-qubit
Clifford+T group. This means that within those su
btheories\, any equality that can be derived using
matrices can also be derived graphically. The ZX-
calculus can thus be applied to a wide range of pr
oblems in quantum information and quantum foundati
ons\, from the analysis of quantum non-locality to
the verification of measurement-based quantum com
putation and error-correcting codes. We also show
how to construct a ZX-like graphical calculus for
Spekkens' toy bit theory\, a local hidden variable
theory which is nevertheless very similar to stab
ilizer quantum mechanics\, and give its associated
completeness proof. Hence Spekkens' toy bit theor
y and stabilizer quantum mechanics -- which is non
-local -- can be analysed and compared entirely gr
aphically.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:William Matthews
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