相关论文: Improved Upper Bounds on the Hermite and KZ Consta…

Module Learning with Errors (M-LWE) based key reconciliation mechanisms (KRM) can be viewed as quantizing an M-LWE sample according to a lattice codebook. This paper describes a generic M-LWE-based KRM framework, valid for any dimensional…

A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called…

We expand on recent exciting work of Debris-Alazard, Ducas, and van Woerden [Transactions on Information Theory, 2022], which introduced the notion of basis reduction for codes, in analogy with the extremely successful paradigm of basis…

A concise theoretical framework, the $\textit{partial}$ Gauss-Hermite quadrature (pGHQ), is established for constructing on-node lattices of the lattice Boltzmann (LB) method under a Cartesian coordinate system. Comparing with existing…

We present some aspects of high precision calculations in the context of Lattice Quantum Field Theory. This work is a collection of three studies done during my Ph.D. period. First we present how to use the reweighting technique to…

An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers.…

Over the last years, novel low-complexity approaches to the equalization of MIMO channels have gained much attention. Thereby, methods based on lattice basis reduction are of special interest, as they achieve the optimum diversity order. In…

Complexity plays a very important part in quantum computing and simulation where it acts as a measure of the minimal number of gates that are required to implement a unitary circuit. We study the lower bound of the complexity [Eisert, Phys.…

We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond…

We study the low temperature limit of lattice QCD by using a reduction formula for a fermion determinant. The reduction formula, which is useful in finite density lattice QCD simulations, contains a reduced matrix defined as the product of…

The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…

Some recent developments in the calculation of weak matrix elements on the lattice are reviewed. In particular, we concentrate on the application of MPSTV non-perturbative renormalization method to the operators relevant to kaon physics.…

The concept of periodic boundary conditions (PBCs) is immensely significant in treating an ideal lattice of infinite extent as a finite lattice. An explicit usage of PBCs is often found missing in undergraduate texts on analytical treatment…

Lattice codes with optimal decoding coefficient are capacity-achieving when dimension $N \rightarrow \infty$. In communications systems, finite dimensional lattice codes are considered, where the optimal decoding coefficients may still fail…

Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods…

This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…

A finite-size technique is employed to compute the normalization constant $Z_A$ of the isovector axial current in lattice QCD. The calculation is carried out in the quenched approximation for values of the bare gauge coupling $g_0$ ranging…

We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study…

In this short note we give incremental algorithms for the following lattice problems: finding a basis of a lattice, computing the successive minima, and determining the orthogonal decomposition. We prove an upper bound for the number of…

Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…