Transversality versus Universality for Additive Quantum Codes
Abstract
Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be {\em universal}; codes with such a universal, transversal gate set have been widely desired for efficient faulttolerant quantum computation. We study the structure of GF(4)additive quantum codes and prove that no universal set of transversal logic operations exists for these codes. This result strongly supports the idea that additional primitive operations, based for example on quantum teleportation, are necessary to achieve universal faulttolerant computation on additive codes.
 Publication:

arXiv eprints
 Pub Date:
 June 2007
 arXiv:
 arXiv:0706.1382
 Bibcode:
 2007arXiv0706.1382Z
 Keywords:

 Quantum Physics
 EPrint:
 12 pages