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SUMMARY:Completeness results for graphical quantum process languages - Mir
 iam Backens (University of Bristol)
DTSTART:20151029T141500Z
DTEND:20151029T151500Z
UID:TALK61130@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:From Feynman diagrams via Penrose graphical notation to quantu
 m circuits\, graphical languages are widely used in quantum theory and oth
 er areas of theoretical physics. The category-theoretical approach to quan
 tum mechanics yields a new set of graphical languages\, which allow rigoro
 us and intuitive pictorial reasoning about quantum systems and processes. 
 One such language is the ZX-calculus\, which is built up of elements corre
 sponding to maps in the computational and the Hadamard basis. We show that
  this graphical language is complete for stabilizer quantum mechanics and 
 for the single-qubit Clifford+T group. This means that within those subthe
 ories\, any equality that can be derived using matrices can also be derive
 d graphically. The ZX-calculus can thus be applied to a wide range of prob
 lems in quantum information and quantum foundations\, 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-li
 ke graphical calculus for Spekkens' toy bit theory\, a local hidden variab
 le theory which is nevertheless very similar to stabilizer quantum mechani
 cs\, and give its associated completeness proof. Hence Spekkens' toy bit t
 heory and stabilizer quantum mechanics -- which is non-local -- can be ana
 lysed and compared entirely graphically.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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