Assume now that a fraction of the entries of Af are corrupted in a completely arbitrary fashion by an error e. We do not know which entries are affected nor do we know how they are affected. Is it possible to recover f exactly from the corrupted m-dimensional vector y = Af + e?
Combining linear programming method and error correction, using the structure of a multiple-criteria and multiple-constraint levels linear programming (MC2LP), which allows two alterable cutoffs, two types of error can be systematically corrected. Therefore, in this paper, we pose a new MC2LP ...
A more powerful error correction code is the convolutional code, which does not have a fixed codeword length and is thus different from the linear block code. In the convolutional code, memory is introduced by streaming the input information bits through registers. Take the structure in Fig. 2....
Calderbank AR, Rains EM, Shor PW, Sloane NJA (1997) Quantum error correction via codes over GF(4). In: Proceedings of IEEE International Symposium on Information Theory Grassl M, Beth T, Pellizzari T (1997) Codes for the quantum erasure channel. Phys Rev A 56(1):33–38. https://doi...
A fast Minimum-Weight Perfect Matching (MWPM) solver for Quantum Error Correction (QEC) Please seeour tutorial for a quick explanation and some Python demos. Our paper is out on arXiv!https://arxiv.org/abs/2305.08307 Key Features
(decoherence) are major obstacles for performing quantum computation and historically many great efforts have been made on reducing such effects39,40. One of the traditional and representative schemes for this is the quantum-error-correction (QEC) coding5,8,10,11,17,41,42,43,44. Another ...
Error correction codes are usually divided into two categories: block codes and convolution codes. Hamming codes, Bose-Chaudur-Hocquenghem(BCH) codes, Reed-Solomon(RS) codes, and Low-density parity-check (LDPC) codes are most notable block codes and have been widely used in communication, ...
These QPUs are accessible via the LeapTM quantum cloud service. The validity and limitations of a critical-phenomena-based error-correction methodology are thoroughly explored for the 1D model in “Methods—Critical and post-critical dynamics of the transverse field Ising chain”. We compare to ...
FRðRcLovS N S ES LðΨLRÞ; HL 1RÞ; quantum error correction via bounded reference frames. Phys. Rev. Res. 4, 023107 (2022). (50) where jΨLRi ¼ p1ffiffiffi dL PdL i¼1 jiL ijiR i is a maximally entanglement state between the logical system L and a ...
An enhanced forward error correction system is disclosed. Transmitted data is encoded into codewords in multiple dimensions. The decoding of received data by a decoder is