https://doi.org/10.1140/epjc/s10052-017-5246-2
Regular Article - Theoretical Physics
New construction of quantum error-avoiding codes via group representation of quantum stabilizer codes
1
College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, 325035, China
2
National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China
3
Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous Services, University of Science and Technology Beijing, Beijing, 100083, China
4
Department of Computer Science, University of Texas at San Antonio, San Antonio, TX, 78249, USA
5
Key Laboratory of Cognitive Radio and Information Processing, Guilin University of Electronic Technology, Ministry of Education, Guilin, 541004, China
* e-mail: xhl_xiaohailin@163.com
Received:
16
February
2017
Accepted:
22
September
2017
Published online:
6
October
2017
In quantum computing, nice error bases as generalization of the Pauli basis were introduced by Knill. These bases are known to be projective representations of finite groups. In this paper, we propose a group representation approach to the study of quantum stabilizer codes. We utilize this approach to define decoherence-free subspaces (DFSs). Unlike previous studies of DFSs, this type of DFSs does not involve any spatial symmetry assumptions on the system-environment interaction. Thus, it can be used to construct quantum error-avoiding codes (QEACs) that are fault tolerant automatically. We also propose a new simple construction of QEACs and subsequently develop several classes of QEACs. Finally, we present numerical simulation results encoding the logical error rate over physical error rate on the fidelity performance of these QEACs. Our study demonstrates that DFSs-based QEACs are capable of providing a generalized and unified framework for error-avoiding methods.
© The Author(s), 2017
