Computer Science – Logic in Computer Science
Scientific paper
2011-03-14
EPTCS 52, 2011, pp. 34-48
Computer Science
Logic in Computer Science
In Proceedings HPC 2010, arXiv:1103.2268
Scientific paper
10.4204/EPTCS.52.4
Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they embody generalized symmetries of the structure of quantum operations, which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One such calculus takes the GHZ and W states as its basic generators. Here we show that this language allows one to encode standard rational calculus, with the GHZ state as multiplication, the W state as addition, the Pauli X gate as multiplicative inversion, and the Pauli Z gate as additive inversion.
Coecke Bob
Kissinger Aleks
Merry Alex
Roy Shibdas
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