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

[Gus Gutoski]

*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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