The non-existence of a [[13,5,4]] quantum stabilizer code
نویسندگان
چکیده
We solve one of the oldest problems in the theory of quantum stabilizer codes by proving the non-existence of quantum [[13,5,4]]-codes.
منابع مشابه
Constacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملAchievable rates for the Gaussian quantum channel
We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quan...
متن کاملNon-stabilizer quantum codes from Abelian subgroups of the error group
This paper is motivated by the computer-generated nonadditive code described in Rains et al [RHSN97]. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example. Furthermore, we give a general strategy of constructing good nonstabilizer codes from good stabilizer codes and give some explicit constructions and asymptotically good nonstabilizer codes. ...
متن کاملUniversal Fault-Tolerant Gates on Concatenated Stabilizer Codes
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of nontransversal, yet still fault-tolerant, gates that work directly on sma...
متن کاملQuantum Stabilizer Codes from Toric Varieties
A.R. Calderbank [1], P.W. Shor [2] and A.M. Steane [3] produced quantum stabilizer codes from linear codes containing their dual codes. A. Ashikhmin, S. Litsyn and M.A. Tsfasman in [4] used the construction to obtain asymptotically good quantum codes fra codes on algebraic curves. In [5] the author developed methods to construct linear error correcting codes from toric varieties and derived the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 57 شماره
صفحات -
تاریخ انتشار 2011