Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
Quantum Physics
2011-03-18 v1
Abstract
A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize our work to show that for subsystem stabilizer codes in dimensional Hilbert space, such a universal set of transversal gates cannot exist for even one encoded qudit, for any dimension , prime or nonprime. This result strongly supports the idea that other primitives, such as quantum teleportation, are necessary for universal fault-tolerant quantum computation, and may be an important factor for fault tolerance noise thresholds.
Keywords
Cite
@article{arxiv.0801.2360,
title = {Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit},
author = {Xie Chen and Hyeyoun Chung and Andrew W. Cross and Bei Zeng and Isaac L. Chuang},
journal= {arXiv preprint arXiv:0801.2360},
year = {2011}
}
Comments
16 pages, 3 figures