相关论文: Lifting a CSS code via its handlebody realization
By leveraging quantum-mechanical properties like superposition, entanglement, and interference, quantum computing (QC) offers promising solutions for problems that classical computing has not been able to solve efficiently, such as drug…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…
Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to…
We would like to better understand the fundamental cone of Tanner graphs derived from finite projective planes. Towards this goal, we discuss bounds on the AWGNC and BSC pseudo-weight of minimal pseudo-codewords of such Tanner graphs, on…
With the rise of remote work and collaboration, compression of screen content images (SCI) is becoming increasingly important. While there are efficient codecs for natural images, as well as codecs for purely-synthetic images, those SCIs…
We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat…
We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads $\mathsf{BV}$ and $\mathsf{HyCom}$, and the top$-2$ weight cohomology of the Feynman transforms of $D\mathsf{BV}$ and $\mathsf{Grav}$. Using a result of…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
A potential advantage of quantum machine learning stems from the ability of encoding classical data into high dimensional complex Hilbert space using quantum circuits. Recent studies exhibit that not all encoding methods are the same when…
Homeomorphism types of compression bodies form the vertices of a graph where two vertices are joined by an edge if one compression body is obtained by gluing a $2$-handle onto the other. Motivated by earlier work of Lackenby and Purcell on…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
The geometric measure, the logarithmic robustness and the relative entropy of entanglement are proved to be equal for a stabilizer quantum codeword. The entanglement upper and lower bounds are determined with the generators of code. The…
We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric…
We review methods used in recent works for constructing handlebody solutions of Einstein's equations in 2+1 dimensions. Additionally, we provide a Mathematica package for computing the action and the boundary moduli of these solutions in a…
We present CV4Code, a compact and effective computer vision method for sourcecode understanding. Our method leverages the contextual and the structural information available from the code snippet by treating each snippet as a…
Scalable image coding for both humans and machines is a technique that has gained a lot of attention recently. This technology enables the hierarchical decoding of images for human vision and image recognition models. It is a highly…
In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
Sewing patterns, the essential blueprints for fabric cutting and tailoring, act as a crucial bridge between design concepts and producible garments. However, existing uni-modal sewing pattern generation models struggle to effectively encode…