episciences.org_3961_1634932078
1634932078
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Logical Methods in Computer Science
1860-5974
12
22
2020
Volume 16, Issue 4
Towards a Minimal Stabilizer ZX-calculus
Miriam
Backens
Simon
Perdrix
Quanlong
Wang
The stabilizer ZX-calculus is a rigorous graphical language for reasoning
about quantum mechanics. The language is sound and complete: one can transform
a stabilizer ZX-diagram into another one using the graphical rewrite rules if
and only if these two diagrams represent the same quantum evolution or quantum
state. We previously showed that the stabilizer ZX-calculus can be simplified
by reducing the number of rewrite rules, without losing the property of
completeness [Backens, Perdrix & Wang, EPTCS 236:1--20, 2017]. Here, we show
that most of the remaining rules of the language are indeed necessary. We do
however leave as an open question the necessity of two rules. These include,
surprisingly, the bialgebra rule, which is an axiomatisation of
complementarity, the cornerstone of the ZX-calculus. Furthermore, we show that
a weaker ambient category -- a braided autonomous category instead of the usual
compact closed category -- is sufficient to recover the meta rule 'only
connectivity matters', even without assuming any symmetries of the generators.
12
22
2020
3961
arXiv:1709.08903
10.23638/LMCS-16(4:19)2020
https://lmcs.episciences.org/3961