Related papers: RG decimation-based approach to confinement and co…
Quantum simulation has shown great potential in many fields due to its powerful computational capabilities. However, the limited fidelity can lead to a severe limitation on the number of gate operations, which requires us to find optimized…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means…
Hamiltonian Truncation (HT) methods provide a powerful numerical approach for investigating strongly coupled QFTs. In this work, we develop HT techniques to analyse a specific Renormalization Group (RG) flow recently proposed in Refs. [1,…
We investigate Riemannian gradient flows for preparing ground states of a desired Hamiltonian on a quantum device. We show that the number of steps of the corresponding Riemannian gradient descent (RGD) algorithm that prepares a ground…
We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…
For pure SU(2) lattice gauge theory at finite T, by the help of the cooling method, we search for classical (approximate) solutions having non-trivial holonomy at the spatial boundary. We identify various typical objects and provide their…
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…
In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations.…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
Quantifying quantum resources for simulating the fundamental forces of Nature is sensitive to the mapping of gauge fields onto finite quantum computational architectures. When locally truncating lattice gauge theories in the irreducible…
We consider correlation inequalities that follow from the well-known loop equations of LGT, and their analogues in spin systems. They provide a way of bounding long range by short or intermediate range correlations. In several cases the…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…
We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation, and are derived from solving single scenario integer programming subproblems…
This paper presents new low-complexity lattice-decoding algorithms for noncoherent block detection of QAM and PAM signals over complex-valued fading channels. The algorithms are optimal in terms of the generalized likelihood ratio test…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
Simulating quantum circuits (QC) on high-performance computing (HPC) systems has become an essential method to benchmark algorithms and probe the potential of large-scale quantum computation despite the limitations of current quantum…
Basic aspects of a program to put field theories quantized in radial coordinates on the lattice are presented. Only scalar fields are discussed. Simple examples are solved to illustrate the strategy when applied to the 3D Ising model.
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A…
The past years have witnessed impressive advances in electronic structure calculation, especially in the complexity and size of the systems studied, as well as in computation time. Linear scaling methods based on empirical tight-binding…