Optimized Quantum Error-Correction Codes For Experiments

We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the underlying physical system and the available means to manipulate it. The final goal is to obtain optimal decompositions of QEC codes into elementary operations which can be realized with high experimental fidelities. In the first part of this paper, this subject is studied in a general fashion, while in the second part, a system of trapped ions is treated as a concrete example. Adetailed optimization algorithm is explained and various decompositions are presented for the three qubit code, the five qubit code, and the seven qubit Steane code.