19 research outputs found
Quasi-cyclic Hermitian construction of binary quantum codes
In this paper, we propose a sufficient condition for a family of 2-generator
self-orthogonal quasi-cyclic codes with respect to Hermitian inner product.
Supported in the Hermitian construction, we show algebraic constructions of
good quantum codes. 30 new binary quantum codes with good parameters improving
the best-known lower bounds on minimum distance in Grassl's code tables
\cite{Grassl:codetables} are constructed
New Codes on Graphs Constructed by Connecting Spatially Coupled Chains
A novel code construction based on spatially coupled low-density parity-check
(SC-LDPC) codes is presented. The proposed code ensembles are described by
protographs, comprised of several protograph-based chains characterizing
individual SC-LDPC codes. We demonstrate that code ensembles obtained by
connecting appropriately chosen SC-LDPC code chains at specific points have
improved iterative decoding thresholds compared to those of single SC-LDPC
coupled chains. In addition, it is shown that the improved decoding properties
of the connected ensembles result in reduced decoding complexity required to
achieve a specific bit error probability. The constructed ensembles are also
asymptotically good, in the sense that the minimum distance grows linearly with
the block length. Finally, we show that the improved asymptotic properties of
the connected chain ensembles also translate into improved finite length
performance.Comment: Submitted to IEEE Transactions on Information Theor
A characterization of entanglement-assisted quantum low-density parity-check codes
As in classical coding theory, quantum analogues of low-density parity-check
(LDPC) codes have offered good error correction performance and low decoding
complexity by employing the Calderbank-Shor-Steane (CSS) construction. However,
special requirements in the quantum setting severely limit the structures such
quantum codes can have. While the entanglement-assisted stabilizer formalism
overcomes this limitation by exploiting maximally entangled states (ebits),
excessive reliance on ebits is a substantial obstacle to implementation. This
paper gives necessary and sufficient conditions for the existence of quantum
LDPC codes which are obtainable from pairs of identical LDPC codes and consume
only one ebit, and studies the spectrum of attainable code parameters.Comment: 7 pages, no figures, final accepted version for publication in the
IEEE Transactions on Information Theor
Quantum error correction protects quantum search algorithms against decoherence
When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10-3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered