Graphical quantum Clifford-encoder compilers from the ZX calculus

Understand

We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus.

• Specifically, we develop a canonical form in the ZX calculus and prove canonicity as well as efficient reducibility of any Clifford encoder into the canonical form.
• The diagrams produced by our compiler visualize information propagation and entanglement structure of the encoder, revealing properties that may be obscured in the circuit or stabilizer-tableau representation.
• Consequently, our canonical representation may be an informative technique for the design of new stabilizer quantum codes via graph theory analysis.