# The ZX-calculus is incomplete for quantum mechanics

arXiv: https://arxiv.org/abs/1404.3633 · HTML: https://mlsanity.com/paper/1404.3633/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2014.

## Built on by (most cited first, 1 of 1)

- [Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)](https://mlsanity.com/paper/2102.10984/) (2021)

## Abstract (arXiv)

We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete.