An application of Khovanov homology to quantum codes

نویسنده

  • Benjamin Audoux
چکیده

We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters 32`+1 √ 8π` ; 1; 2 ; unlink codes with asymptotical parameters √ 3 2π`6 ; 2; 2 and (2, `)–torus link codes with asymptotical parameters ~n; 1; dn where dn > √ n 1.62 .

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Link Homology Theories from Extended Cobordisms

Abstract. This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2–dimensional cobordisms by taking into account their embedding into R. Secondly, we extend the underlying cobordism category to a 2–category, where the usual relations hold up to ...

متن کامل

A SPECTRAL SEQUENCE FOR KHOVANOV HOMOLOGY WITH AN APPLICATION TO (3, q)-TORUS LINKS

A spectral sequence converging to Khovanov homology is constructed which is applied to calculate the rational Khovanov homology of (3, q)-torus links.

متن کامل

Khovanov Homology, Open Books, and Tight Contact Structures

We define the reduced Khovanov homology of an open book (S, φ), and we identify a distinguished “contact element” in this group which may be used to establish the tightness of contact structures compatible with (S, φ). Our construction generalizes the relationship between the reduced Khovanov homology of a link and the Heegaard Floer homology of its branched double cover. As an application, we ...

متن کامل

Monopole Floer Homology, Link Surgery, and Odd Khovanov Homology

Monopole Floer Homology, Link Surgery, and Odd Khovanov Homology Jonathan Michael Bloom We construct a link surgery spectral sequence for all versions of monopole Floer homology with mod 2 coefficients, generalizing the exact triangle. The spectral sequence begins with the monopole Floer homology of a hypercube of surgeries on a 3-manifold Y , and converges to the monopole Floer homology of Y i...

متن کامل

H-thick Knots in Khovanov Homology

We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee’s map Φ. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that specific families of such knots cannot be detected by Khovanov’s thickness criter...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1307.4677  شماره 

صفحات  -

تاریخ انتشار 2013