Towards Local Testability for Quantum Coding
LEVERRIER, Anthony
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
LONDE, Vivien
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
LEVERRIER, Anthony
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
LONDE, Vivien
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
< Reduce
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]
Language
en
Communication dans un congrès
This item was published in
ITCS 2021 - 12th Conference on Innovations in Theoretical Computer Science, 2021-01-06, Washington / Virtual. vol. 185, p. 65:1--65:11
Schloss Dagstuhl
English Abstract
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n > p) and stabilizer constraints with faces of dimension (p ± 1). The quantum code obtained ...Read more >
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n > p) and stabilizer constraints with faces of dimension (p ± 1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into N = 2 n−p−1 n p physical qubits and displays local testability with a soundness of Ω(1/ log(N)) beating the current state-of-the-art of 1/ log 2 (N) due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors. We then extend this code family by considering the quotient of the n-cube by arbitrary linear classical codes of length n. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be constant, similarly to the ordinary n-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension.Read less <
English Keywords
Quantum error correcting code
Origin
Hal imported