Related papers: Quadratic Modelings of Syndrome Decoding
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…
In recent years, copositive programming has received significant attention for its ability to model hard problems in both discrete and continuous optimization. Several relaxations of copositive programs based on semidefinite programming…
Quadratization for partial differential equations (PDEs) is a process that transforms a nonquadratic PDE into a quadratic form by introducing auxiliary variables. This symbolic transformation has been used in diverse fields to simplify the…
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance…
The paper investigates the problem of fitting protein complexes into electron density maps. They are represented by high-resolution cryoEM density maps converted into overlapping matrices and partly show a structure of a complex. The…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
A major obstacle for quantum optimizers is the reformulation of constraints as a quadratic unconstrained binary optimization (QUBO). Current QUBO translators exaggerate the weight $M$ of the penalty terms. Classically known as the "Big-$M$"…
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass…
We adress the problem of the algebraic decoding of any cyclic code up to the true minimum distance. For this, we use the classical formulation of the problem, which is to find the error locator polynomial in terms of the syndroms of the…
Triangular decomposition with different properties has been used for various types of problem solving, e.g. geometry theorem proving, real solution isolation of zero-dimensional polynomial systems, etc. In this paper, the concepts of strong…
The Syndrome Decoding problem is at the core of many code-based cryptosystems. In this paper, we study ternary Syndrome Decoding in large weight. This problem has been introduced in the Wave signature scheme but has never been thoroughly…
We consider the problem of approximating nonconvex quadratic optimization with ellipsoid constraints (ECQP). We show some SDP-based approximation bounds for special cases of (ECQP) can be improved by trivially applying the extened Pataki's…
The unconstrained binary quadratic programming (UBQP) problem is a class of problems of significant importance in many practical applications, such as in combinatorial optimization, circuit design, and other fields. The positive…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
Syndrome-based neural decoding (SBND) has emerged as a promising deep learning approach for soft-decision decoding of high-rate, short-length codes. However, this approach still has substantial room for improvement. In this paper, we show…
In this paper, we consider a class of nonconvex complex quadratic programming (CQP) problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first…
Communication-reduction techniques are a popular way to improve scalability in data-parallel training of deep neural networks (DNNs). The recent emergence of large language models such as GPT has created the need for new approaches to…