Related papers: Predicting Module-Lattice Reduction
In this paper, we show that for each lattice basis, there exists an equivalent basis which we describe as ``strongly reduced''. We show that bases reduced in this manner exhibit rather ``short'' basis vectors, that is, the length of the…
In this paper we extend the estimate of the value of the lattice spacing a in units of the r0 scale at values of the bare coupling larger than those available. By using results from the computation of the renormalised coupling in the…
The rapid growth of hardware vulnerabilities has created an urgent need for systematic and scalable analysis methods. Unlike software flaws, which are often patchable post-deployment, hardware weaknesses remain embedded across product…
We study the decay B --> K l^+ l^- for l = e,mu,tau with a softly recoiling kaon, that is, for high dilepton invariant masses sqrt{q^2} of the order of the b-quark mass. This kinematic region can be treated within an operator product…
The Berezinskii-Kosterlitz-Thouless (BKT) transition is a typical topological phase transition defined between binding and unbinding states of vortices and antivortices, which is not accompanied by spontaneous symmetry breaking. It is known…
We present new results of our ongoing project toward a precision determination of the kaon $B$ parameter with the Kogut-Susskind quark action in quenched QCD. New results taken at $\beta$=6.4 and $\beta=5.7$ suggest that an apparently…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties…
Fine-tuning is a crucial process for adapting large language models (LLMs) to diverse applications. In certain scenarios, such as multi-tenant serving, deploying multiple LLMs becomes necessary to meet complex demands. Recent studies…
Recently, lattice-reduction-aided detectors have been proposed for multiple-input multiple-output (MIMO) systems to give performance with full diversity like maximum likelihood receiver, and yet with complexity similar to linear receivers.…
Quantum spin-lattice systems in low dimensions exhibit a variety of interesting zero-temperature phases, some of which show non-classical (i.e., non-magnetic) long-range orders, such as dimer or trimer valence-bond order. These…
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary…
Generalized bicycle codes (GB codes) represent a promising family of quantum low-density parity-check codes, characterized by high code rates and relatively local qubit connectivity. A subclass of the GB code called bivariate bicycle codes…
The first aim of this work is to characterize when the lattice of all submodules of a module is a direct product of two lattices. In particular, which decompositions of a module $M$ produce these decompositions: the \emph{lattice…
A $\mathbb{Z}^d$-graded differential $R$-module is a $\mathbb{Z}^d$-graded $R$-module $D$ equipped with an endomorphism, $\delta$, that squares to zero. For $R=k[x_1,\ldots,x_d]$, this paper establishes a lower bound on the rank of such a…
Low-bit post-training quantization (PTQ) is a practical route to deploy reasoning-capable LLMs under tight memory and latency budgets, yet it can markedly impair mathematical reasoning (drops up to 69.81% in our harder settings). We address…
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes universal vortex unbinding in many two-dimensional systems, including the paradigmatic XY model. However, most of these systems present a complex interplay between excitations at…
Quantum annealing (QA) is proposed for vector perturbation precoding (VPP) in multiple input multiple output (MIMO) communications systems. The mathematical framework of VPP is presented, outlining the problem formulation and the benefits…
Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in…
Quantization has emerged as a mainstream method for compressing Large Language Models (LLMs), reducing memory requirements and accelerating inference without architectural modifications. While existing research primarily focuses on…