10.23638/LMCS-16(4:19)2020
Backens, Miriam
Miriam
Backens
Perdrix, Simon
Simon
Perdrix
Wang, Quanlong
Quanlong
Wang
Towards a Minimal Stabilizer ZX-calculus
episciences.org
2020
Quantum Physics
Computer Science - Logic in Computer Science
F.1.1
F.3.2
contact@episciences.org
episciences.org
2017-09-27T16:44:07+02:00
2021-01-15T15:51:19+01:00
2020-12-22
eng
Journal article
https://lmcs.episciences.org/3961
arXiv:1709.08903
1860-5974
PDF
1
Logical Methods in Computer Science ; Volume 16, Issue 4 ; 1860-5974
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.