The ZX-calculus is complete for stabilizer quantum mechanics

Miriam Backens
2014 New Journal of Physics  
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics,
more » ... aning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
doi:10.1088/1367-2630/16/9/093021 fatcat:adnoquyv6vbppkdj4bsj5vlane