[quantum-info] PIQuDos seminar Wed Dec10: Miriam Backens

Gus Gutoski ggutoski at perimeterinstitute.ca
Wed Dec 10 13:57:50 EST 2014


Reminder: PIQuDos seminar by Miriam Backens today at 4pm in the Time room.

On Fri, Dec 5, 2014 at 10:13 PM, Gus Gutoski <ggutoski at perimeterinstitute.ca
> wrote:

> *Wednesday, Dec. 10th, 2014*
>
> at 4:00 p.m. in Time Room (294)
> *Perimeter Institute Quantum Discussions
> <http://perimeterinstitute.ca/video-library/collection/perimeter-institute-quantum-discussions>*
>  *–* *Completeness Results for Graphical Quantum Process Languages
> <http://perimeterinstitute.ca/seminar/completeness-results-graphical-quantum-process-languages>*
>  -
> *with Miriam Backens, University of Oxford*From Feynman diagrams via
> Penrose graphical notation to quantum circuits, graphical languages are
> widely used in quantum theory and other areas of theoretical physics. The
> category-theoretical approach to quantum mechanics yields a new set of
> graphical languages, which allow rigorous pictorial reasoning about quantum
> systems and processes. One such language is the ZX-calculus, which is built
> up of elements corresponding to maps in the computational and the Hadamard
> basis. This calculus is universal for pure state qubit quantum mechanics,
> meaning any pure state, unitary operation, and post-selected pure
> projective measurement can be represented. It is also sound, meaning any
> graphical rewrite corresponds to a valid equality when translated into
> matrices. While the calculus is not complete for general quantum mechanics,
> I show that it is complete for stabilizer quantum mechanics and for the
> single-qubit Clifford+T group. This means that within those subtheories,
> 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
> problems in quantum information and quantum foundations, from the analysis
> of quantum non-locality to the verification of measurement-based quantum
> computation and error-correcting codes. I also show how to construct a
> ZX-like graphical calculus for Spekkens' toy bit theory and give its
> associated completeness proof.
>
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