Sergey Bravyi, IBM Research
Quantum self-correction in Majorana chains and topological qubits
IBM Research, Yorktown Heights, USA
A big open question in the quantum information theory concerns feasibility of a self-correcting quantum memory. A user of such memory would need quantum computing capability only to write and read information. A long-term passive storage of information can be achieved if the natural low-temperature dynamics of the system limits creation and propagation of errors.
In this talk I will review two toy models of a quantum memory in which certain form of
self-correction can be rigorously proved. The first model, due to Kitaev (2001), describes a quantum wire with unpaired Majorana fermions localized on the boundary. We show that the storage time of the encoded qubit at T=0 can be significantly enhanced by a quenched disorder chosen as a random site-dependent chemical potential. The disorder strongly limits coherent propagation of topological defects due to the Anderson localization phenomenon.
The second model, due to Haah (2011), describes a 3D lattice of qubits with local 8-qubit interactions and a topologically ordered ground state. We show that the thermal diffusion of topological defects in this model is suppressed by logarithmic energy barriers. The maximum storage time that can be achieved at a given temperature T grows exponentially with 1/T2.
[1] S.B. and J. Haah, Phys. Rev. Lett. 107, 150504 (2011)
[2] S.B. and J. Haah, arXiv:1112.3252
[3] S.B. and R. Koenig, arXiv:1108.3845