Transversality versus Universality for Additive Quantum Codes

Understand

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 fault-tolerant 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.