Abstract
A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As shown by Zeng et al. (e-print 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.
- Received 15 January 2008
DOI:https://doi.org/10.1103/PhysRevA.78.012353
©2008 American Physical Society