Superconducting analogue of the parafermion fractional quantum Hall states

Read and Rezayi $Z_k$ parafermion wavefunctions describe $\nu=2+\frac{k}{kM+2}$ fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the $\nu=2/k$ FQH-superconductor heterostructure and find the superconducting analogue of the $Z_k$ parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional (1D) chains each with a pair of counter-propagating modes. We show that by inducing intra-chain pairing and charge preserving backscattering with identical couplings, the 1D chains flow into gapless $Z_{k}$ parafermions when $k< 4$. By studying the effect of inter-chain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a $Z_k$ parafermion conformal field theory. For instance, we find that a $\nu=2/3$ FQH in proximity to a superconductor produces a $Z_3$ parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the $\nu=12/5$ Read-Rezay state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.Comment: 11 pages, 3 figure

Improved Modeling of the Correlation Between Continuous-Valued Sources in LDPC-Based DSC

Accurate modeling of the correlation between the sources plays a crucial role in the efficiency of distributed source coding (DSC) systems. This correlation is commonly modeled in the binary domain by using a single binary symmetric channel (BSC), both for binary and continuous-valued sources. We show that "one" BSC cannot accurately capture the correlation between continuous-valued sources; a more accurate model requires "multiple" BSCs, as many as the number of bits used to represent each sample. We incorporate this new model into the DSC system that uses low-density parity-check (LDPC) codes for compression. The standard Slepian-Wolf LDPC decoder requires a slight modification so that the parameters of all BSCs are integrated in the log-likelihood ratios (LLRs). Further, using an interleaver the data belonging to different bit-planes are shuffled to introduce randomness in the binary domain. The new system has the same complexity and delay as the standard one. Simulation results prove the effectiveness of the proposed model and system.Comment: 5 Pages, 4 figures; presented at the Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 201