Details:
Title  Gr\"obner bases for finitetemperature quantum computing and their complexity.  Author(s)  P.R. Crompton  Type  Article in Journal  Abstract  Following the recent approach of using order domains to construct Gröbner bases from general projective varieties, we examine the parity and timereversal arguments relating to the Wightman axioms of quantum field theory and propose that the definition of associativity in these axioms should be introduced a posteriori to the cluster property in order to generalize the anyon conjecture for quantum computing to indefinite metrics. We then show that this modification, which we define via ideal quotients, does not admit a faithful representation of the Braid group, because the generalized twisted inner automorphisms that we use to reintroduce associativity are only parity invariant for the prime spectra of the exterior algebra. We then use a coordinate prescription for the quantum deformations of toric varieties to show how a faithful representation of the Braid group can be reconstructed and argue that for a degree reverse lexicographic (monomial) ordered Gröbner basis, the complexity class of this problem is bounded quantum polynomial.  ISSN  00222488; 10897658/e 
URL 
http://scitation.aip.org/content/aip/journal/jmp/52/11/10.1063/1.3660379 
Language  English  Journal  J. Math. Phys.  Volume  52  Number  11  Pages  112203, 8  Publisher  American Institute of Physics (AIP), Woodbury, NY  Year  2011  Edition  0  Translation 
No  Refereed 
No 
