Fault-tolerant quantum computation with non-binary systems

Abstract

In this paper, we present the stabilizer transformation formalism under measurements in q-ary systems where q is an odd prime power. Through a clever use of sequential stabilizer manipulations, we can implement several q-ary logical gates in a fault-tolerant way. Furthermore, a randomized fault-tolerant code conversion procedure between arbitrary non-binary stabilizer codes is proposed, in which descendant ancillary qudits are required with growing dimension of systems. Finally, we adapt the idea of stabilizer transformation in the construction of q-ary entanglement-assisted quantum stabilizer codes.