IQI Weekly Seminar

  There is a standard generalization of stabilizer codes to work  with qudits which have prime dimension, and a slightly less standard  generalization for qudits whose dimension is a prime power.  However, for  prime power dimensions, the usual generalization effectively treats the  qudit as multiple prime-dimensional qudits instead of one larger object.  There is a finite field GF(q) with size equal to any prime power, and it  makes sense to label the qudit basis states with elements of the finite  field, but the usual stabilizer codes do not make use of the structure of  the finite field.  I introduce the true GF(q) stabilizer codes, a subset of  the usual prime power stabilizer codes which do make full use of the finite  field structure.  The true GF(q) stabilizer codes have nicer properties than  the usual stabilizer codes over prime power qudits and work with a lifted  Pauli group, which has some interesting mathematical aspects to it.