Related papers: Optimal embedding of hypercube into cylinder
Quantum computing holds transformative potential for various fields, yet its practical application is hindered by the susceptibility to errors. This study makes a pioneering contribution by applying quantum error correction codes (QECCs)…
Commonly, for homogenization of fibrous media, fibers are approximated by ellipsoidal inclusions. Indeed, the solution of Eshelby's problem for an ellipsoid is well-known analytically. However, for a cylinder, the analytical solution is not…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
Effective conductivity of a 2D composite corresponding to the regular hexagonal arrangement of superconducting disks is expressed in the form of a long series in the volume fraction of ideally conducting disks. According to our calculations…
We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a…
The central levels problem asserts that the subgraph of the $(2m+1)$-dimensional hypercube induced by all bitstrings with at least $m+1-\ell$ many 1s and at most $m+\ell$ many 1s, i.e., the vertices in the middle $2\ell$ levels, has a…
This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
A theoretical study of free space coupling to high-Q whispering gallery modes both in circular and deformed microcavities are presented. In the case of a circular cavity, both analytical solutions and asymptotic formulas are derived. The…
Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems…
Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…
Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid…
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for…
In steganography, we always hope to maximize the embedding payload subject to an upper-bounded distortion. We need suitable distortion measurement to evaluate the embedding impact. However, different distortion functions exposes different…
In the recent years, there has been active research on self-orthogonal embeddings of linear codes since they yielded some optimal self-orthogonal codes. LCD codes have a trivial hull so they are counterparts of self-orthogonal codes. So it…
This paper introduces a methodology based on Euclidean information theory to investigate local properties of secure communication over discrete memoryless wiretap channels. We formulate a constrained optimization problem that maximizes a…
Aims: Try to prove the $n$-dimensional balanced hypercube $BH_n$ is $(2n-2)$-fault-tolerant-prescribed hamiltonian laceability. Methods: Prove it by induction on $n$. It is known that the assertation holds for $n\in\{1,2\}$. Assume it holds…
We discuss the scalability of superconducting quantum computers, especially in a wiring problem. The number of wiring inside a cryostat is almost proportional to the number of qubits in current wiring architectures. We introduce regularity,…
Given a constant $k>1$ and a real valued function $K$ on the hyperbolic plane $\mathbb H^2$, we study the problem of finding, for any $\epsilon\approx 0$, a closed and embedded curve $u^\epsilon $ in $\mathbb H^2$ having geodesic curvature…