7 research outputs found
Enhanced Feedback Iterative Decoding of Sparse Quantum Codes
Decoding sparse quantum codes can be accomplished by syndrome-based decoding
using a belief propagation (BP) algorithm.We significantly improve this
decoding scheme by developing a new feedback adjustment strategy for the
standard BP algorithm. In our feedback procedure, we exploit much of the
information from stabilizers, not just the syndrome but also the values of the
frustrated checks on individual qubits of the code and the channel model.
Furthermore we show that our decoding algorithm is superior to belief
propagation algorithms using only the syndrome in the feedback procedure for
all cases of the depolarizing channel. Our algorithm does not increase the
measurement overhead compared to the previous method, as the extra information
comes for free from the requisite stabilizer measurements.Comment: 10 pages, 11 figures, Second version, To be appeared in IEEE
Transactions on Information Theor
Trapping Sets of Quantum LDPC Codes
Iterative decoders for finite length quantum low-density parity-check (QLDPC)
codes are attractive because their hardware complexity scales only linearly
with the number of physical qubits. However, they are impacted by short cycles,
detrimental graphical configurations known as trapping sets (TSs) present in a
code graph as well as symmetric degeneracy of errors. These factors
significantly degrade the decoder decoding probability performance and cause
so-called error floor. In this paper, we establish a systematic methodology by
which one can identify and classify quantum trapping sets (QTSs) according to
their topological structure and decoder used. The conventional definition of a
TS from classical error correction is generalized to address the syndrome
decoding scenario for QLDPC codes. We show that the knowledge of QTSs can be
used to design better QLDPC codes and decoders. Frame error rate improvements
of two orders of magnitude in the error floor regime are demonstrated for some
practical finite-length QLDPC codes without requiring any post-processing.Comment: Revised version - 19 pages, 12 figures - Accepted for publication in
Quantu
High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find