Results 11 to 20 of about 172,944 (286)
PRX Quantum, 2022 We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a [[10,1,2]] code that is the smallest-known stabilizer code with a fault ...
Michael Vasmer, Aleksander Kubica
doaj +4 more sources
Application of Constacyclic codes to Quantum MDS Codes [PDF]
IEEE Transactions on Information Theory, 2014 Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction ...
Chen, Bocong, Ling, San, Zhang, Guanghui
core +3 more sources
On optimal quantum codes [PDF]
International Journal of Quantum Information, 2003 We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power ...
MacWilliams F. J. +3 more
core +2 more sources
Additive Asymmetric Quantum Codes [PDF]
IEEE Transactions on Information Theory, 2011 We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over $\F_{4}$ are used in the construction of many asymmetric quantum codes over $\F_{4 ...
Ezerman, Martianus Frederic +2 more
core +3 more sources
Quantum Machine Intelligence, 2022 Abstract The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with an approximation method, such as lasso or orthogonal matching pursuit, thus trading off accuracy ...
Yaniv Romano +7 more
openaire +2 more sources
IEEE Transactions on Information Theory, 2022 21 pages, 10 ...
Christophe Vuillot +1 more
openaire +8 more sources
Journal of Algebra Combinatorics Discrete Structures and Applications, 2022 Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a comprehensive database of best known codes (codetables.de) exists which is available online at \cite{codetables}. The same database contains data on best known quantum codes as well, but only for the binary field.
Nuh Aydin, Peihan Liu, Bryan Yoshino
openaire +2 more sources
Parallel Quantum Computation and Quantum Codes [PDF]
SIAM Journal on Computing, 2001 We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or more generally any circuit consisting of controlled-not ...
Cristopher Moore, Martin Nilsson
openaire +3 more sources
2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), 2022 35 pages, v2: added a description of the quadripartite version of the code and an almost matching upper bound for the distance, v3: full version of the extended abstract appearing at FOCS ...
Leverrier, Anthony, Zémor, Gilles
openaire +3 more sources
2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 2015 We present an efficient decoding algorithm for constant rate quantum hypergraph-product LDPC codes which provably corrects adversarial errors of weight $Ω(\sqrt{n})$ for codes of length $n$. The algorithm runs in time linear in the number of qubits, which makes its performance the strongest to date for linear-time decoding of quantum codes.
Leverrier, Anthony +2 more
openaire +3 more sources