相关论文: Constructive Conjugate Codes for Quantum Error Cor…
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…
Computing the closed convex envelope or biconjugate is the core operation that bridges the domain of nonconvex with convex analysis. We focus here on computing the conjugate of a bivariate piecewise quadratic function defined over a…
Subsystem codes are the most versatile class of quantum error-correcting codes known to date that combine the best features of all known passive and active error-control schemes. The subsystem code is a subspace of the quantum state space…
This paper considers the joint-decoding (JD) problem for finite-state channels (FSCs) and low-density parity-check (LDPC) codes. In the first part, the linear-programming (LP) decoder for binary linear codes is extended to JD of…
Conjucyclic codes are part of a family of codes that includes cyclic, constacyclic, and quasi-cyclic codes, among others. Despite their importance in quantum error correction, they have not received much attention in the literature. This…
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…
Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to…
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…
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…
It is generally unclear whether smaller codes can be "concatenated" to systematically create quantum LDPC codes or their sparse subsystem code cousins where the degree of the Tanner graph remains bounded while increasing the code distance.…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear complementary pairs of quasi-cyclic and quasi-twisted codes…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
In sphere of research of discrete optimization algorithms efficiency the important place occupies a method of polynomial reducibility of some problems to others with use of special purpose components. In this paper a novel method of compact…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
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,…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
Conjugate degradable channels are channels whose quantum capacity is calculable. They were defined and studied in [1] where, however, only channels that are both degradable and conjugate degradable were found. In this paper we bring the…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…