Abstract
In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in $PG(3,9)$ and $PG(4,9)$ are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code with $d=4$ , we obtain 278 quantum error-correcting codes. Most of these results break the GV bound, and a number of them are optimal quantum codes or have improved parameters.
Highlights
C OMPARED to classic computing, quantum computing has overwhelming superiority in terms of operation and security
Quantum error correction is essential in quantum computing
In 1995, Shor [2] formulated the theory of quantum errorcorrecting codes (QECCs) and presented an example of a quantum [[9, 1, 3]]-code that could correct one error
Summary
C OMPARED to classic computing, quantum computing has overwhelming superiority in terms of operation and security. Lemma 1: [4] If C is a q2-ary linear code of length n, dimension k and dual distance d⊥, which is self-orthogonal with respect to the Hermitian inner product, there exists a pure quantum error-correcting code with parameters [[n, n − 2k, d⊥]]q. One central theme in quantum error-correction is the construction of QECCs with optimal parameters. Many 2-ary QEECs of optimal parameters are constructed by quantum caps in P G(r, 4) (see [9]–[15]). We analyze the optimality of the constructed quantum codes and present conclusions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
