Graph state basis for Pauli Channels

We introduce graph state basis diagonalization to calculate the coherent information of a quantum code passing through a Pauli channel. The scheme is 5000 times faster than the best known one for some concatenated repetition codes, providing us a practical constructive way of approaching the quantum capacity of a Pauli channel. The calculation of the coherent information of non-additive quantum code can also be greatly simplified in graph state basis.Comment: 5 page

Computational Discovery of A New Rhombohedral Diamond Phase

We identify by first-principles calculations a new diamond phase in R¯3c (D63d) symmetry, which has a 16-atom rhombohedral primitive cell, thus termed R16 carbon. This rhombohedral diamond comprises a characteristic all-sp3 six-membered-ring bonding network, and it is energetically more stable than previously identified diamondlike six-membered-ring bonded BC8 and BC12 carbon phases. A phonon mode analysis verifies the dynamic structural stability of R16 carbon, and electronic band calculations reveal that it is an insulator with a direct band gap of 4.45 eV. Simulated x-ray diffraction patterns provide an excellent match to recently reported distinct diffraction peaks found in milled fullerene soot, suggesting a viable experimental synthesis route. These findings pave the way for further exploration of this new diamond phase and its outstanding properties