Grobner Bases for Finite-temperature Quantum Computing and their Complexity
Quantum Physics
2015-05-19 v1
Abstract
Following the recent approach of using order domains to construct Grobner bases from general projective varieties, we examine the parity and time-reversal arguments relating de Witt and Lyman's assertion that all path weights associated with homotopy in dimensions d <= 2 form a faithful representation of the fundamental group of a quantum system. We then show how the most general polynomial ring obtained for a fermionic quantum system does not, in fact, admit a faithful representation, and so give a general prescription for calcluating Grobner bases for finite temperature many-body quantum system and show that their complexity class is BQP.
Cite
@article{arxiv.1008.4055,
title = {Grobner Bases for Finite-temperature Quantum Computing and their Complexity},
author = {P. R. Crompton},
journal= {arXiv preprint arXiv:1008.4055},
year = {2015}
}