517,920 research outputs found
Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
One of the leading quantum computing architectures is based on the
two-dimensional (2D) surface code. This code has many advantageous properties
such as a high error threshold and a planar layout of physical qubits where
each physical qubit need only interact with its nearest neighbours. However,
the transversal logical gates available in 2D surface codes are limited. This
means that an additional (resource intensive) procedure known as magic state
distillation is required to do universal quantum computing with 2D surface
codes. Here, we examine three-dimensional (3D) surface codes in the context of
quantum computation. We introduce a picture for visualizing 3D surface codes
which is useful for analysing stacks of three 3D surface codes. We use this
picture to prove that the and gates are transversal in 3D surface
codes. We also generalize the techniques of 2D surface code lattice surgery to
3D surface codes. We combine these results and propose two quantum computing
architectures based on 3D surface codes. Magic state distillation is not
required in either of our architectures. Finally, we show that a stack of three
3D surface codes can be transformed into a single 3D color code (another type
of quantum error-correcting code) using code concatenation.Comment: 23 pages, 24 figures, v2: published versio
How Fast Can Dense Codes Achieve the Min-Cut Capacity of Line Networks?
In this paper, we study the coding delay and the average coding delay of
random linear network codes (dense codes) over line networks with deterministic
regular and Poisson transmission schedules. We consider both lossless networks
and networks with Bernoulli losses. The upper bounds derived in this paper,
which are in some cases more general, and in some other cases tighter, than the
existing bounds, provide a more clear picture of the speed of convergence of
dense codes to the min-cut capacity of line networks.Comment: 15 pages, submitted to IEEE ISIT 201
On asymptotically good ramp secret sharing schemes
Asymptotically good sequences of linear ramp secret sharing schemes have been
intensively studied by Cramer et al. in terms of sequences of pairs of nested
algebraic geometric codes. In those works the focus is on full privacy and full
reconstruction. In this paper we analyze additional parameters describing the
asymptotic behavior of partial information leakage and possibly also partial
reconstruction giving a more complete picture of the access structure for
sequences of linear ramp secret sharing schemes. Our study involves a detailed
treatment of the (relative) generalized Hamming weights of the considered
codes
Cross Continental Readings of Visual Narratives: An analysis of Six Books in the New Zealand PictureBook Collection
This article argues that, by analyzing the ways in which illustrators use certain visual codes, we can learn much about a country's history/culture and demonstrates this by analyzing the visual narratives of six picture books from the New Zealand Picture Book Collection (NZPBC) Emphasis is placed on how the front covers-which introduce both the stories and the new culture to young readers-are used to facilitate cultural understanding by focusing on Intercultural stimuli/cultural exchanges; respecting beliefs/values; observing cultural lifestyles, sharing visual imagery and discussing the interplay between text and imag
A Note on the Injection Distance
Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding
for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory,
{54(8), 2008] that the network coding counterpart of Gabidulin codes performs
asymptotically optimal with respect to the subspace distance. Recently, Silva
and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for
Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory,
ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed
picture of what happens in noncoherent network coding. We show that the above
codes are also asymptotically optimal with respect to this distance
Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero
Gabidulin codes over fields of characteristic zero were recently constructed by Augot et al., whenever the Galois group of the underlying field extension is cyclic. In parallel, the interest in sparse generator matrices of Reed–Solomon and Gabidulin codes has increased lately, due to applications in distributed computations. In particular, a certain condition pertaining to the intersection of zero entries at different rows, was shown to be necessary and sufficient for the existence of the sparsest possible generator matrix of Gabidulin codes over finite fields. In this paper we complete the picture by showing that the same condition is also necessary and sufficient for Gabidulin codes over fields of characteristic zero.Our proof builds upon and extends tools from the finite-field case, combines them with a variant of the Schwartz–Zippel lemma over automorphisms, and provides a simple randomized construction algorithm whose probability of success can be arbitrarily close to one. In addition, potential applications for low-rank matrix recovery are discussed
Value World–Pictures and Axiological Codes of Musical Genres
This article explores the possibility of establishing cultural dialogue through the axiological codes of musical genres. Genre here is defined as a worldview and as a component of the world-picture that carries axiological codes. The methodology used here combines culturological, axiological, world-image, and comparative approaches. As a result, we have developed the samples of the typological and national models of the value world-picture based on genre axiological codes. The key conclusions are: it is possible to construct a musical genre world-picture, which reflects the hierarchy of values in the world pictures of different types, and to promote the genre-value world-picture facilitating cultural dialogue.
Keywords: value world-picture, musical genre, axiocode, axiologeme, value hierarch
Majorana dimers and holographic quantum error-correcting codes
Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography
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