zx-calc

WARNING: This project is in a very early state! Main tools are usable (see the list of features below), but may be buggy and/or error-prone.

Contains tools for working in the ZX-calculus, a diagrammatic language for reasoning about linear maps between two-level quantum states.

Features

• Multiple diagram representations
  • Ranked, tensorless ket-bra forms
  • Graph-based forms
  • Render to graphviz
  • Conversion between representations
• Diagram tools
  • Scalar computation
  • Evaluation (based on conversion to ketbra form)
  • Diagram composition/tensoring (partial: untested)
• Diagram simplification (graph-based only)
  • ZX rewrite rules
    • Z/X/HH identity removal
    • Spider fusion
    • Hopf rule
    • "H2-Hopf" rule (identical colors with intervening H-boxes)
    • Spider color change
    • Remove self-loops with single H-boxes
    • Euler-angle expansion of an H-box between two spiders of the same color
    • Color-change and fuse for Z-H-X sandwiches
    • π-commute and fuse for Z-X-Z/X-Z-X sandwiches
    • Heuristic-based general reduction of H-boxes via color change
    • Heuristic-based general reduction of π-spiders via π-commute
    • Bialgebra rule
    • State/effect copying
    • Equivalence of spider-states with ±π/2 phases
  • ZH rewrite rules
    • H-box fusion
    • π-state/effect absorption
    • State/effect explosion through an H-box
    • H-state/effect conversion to Z-state/effect
    • π Z-state/effect copying through H-boxes
    • State/effect expansion of H-boxes with label 1
    • H-box version of the Hopf rule
    • H-box version of the bialgebra rule
    • H-box averaging rule
    • Multiplication rule
    • H-box wire introduction rule (reversed)
  • Single, exhaustive "simplify" (partial: waiting on testing with different strategies)
  • Scalar computation and removal
  • Equality testing via simplification
• Circuits
  • Basic ranked circuit representation
  • Read/write OpenQASM
  • Render to Graphviz
  • Conversion to diagram representations
  • Circuit extraction from diagrams
• Time/space optimization

Helpful resources

• B. Coecke, "Basic ZX-calculus for students and professionals." arXiv:2303.03163
• J. van de Wetering, "ZX-calculus for the working quantum computer scientist." arXiv:2012.13966
• R. Moyard, "Introduction to the ZX-calculus." Pennylane
• H. Bombin et al., "Unifying flavors of fault tolerance with the ZX calculus." arXiv:2303.08829

See also

• PyZX: a Python implementation of the ZX-calculus and its rewrite rules
• QuiZX: a Rust implementation of the above.