Abstract
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 (QM), 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 QM, meaning 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.
Original language | English |
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Article number | 093021 |
Number of pages | 30 |
Journal | New Journal of Physics |
Volume | 16 |
Issue number | 9 |
DOIs | |
Publication status | Published - 17 Sept 2014 |
Keywords
- quantum foundations
- quantum computing
- logic
- graphical calculus
- stabilizer quantum mechanics
- graph states