相关论文: A Modified KZ Reduction Algorithm

This paper proposes a novel matrix quantization method, Binary Quadratic Quantization (BQQ). In contrast to conventional first-order quantization approaches, such as uniform quantization and binary coding quantization, that approximate…

A cluster algorithm is presented for the $Z_2$ Kalb-Ramond plaquette model in four dimensions which dramatically reduces critical slowing. The critical exponent $z$ is reduced from $ z>2$ (standard Metropolis algorithm) to $z= 0.32\pm0.06$.…

This paper develops a fully discrete Fourier spectral Galerkin (FSG) method for the fractional Zakharov--Kuznetsov (fZK) equation posed on a two-dimensional periodic domain. The equation generalizes the classical ZK model by replacing the…

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…

The paper proposes an improved quantum associative algorithm with distributed query based on model proposed by Ezhov et al. We introduce two modifications of the query that optimized data retrieval of correct multi-patterns simultaneously…

We present a new framework for designing worst-case to average-case reductions. For a large class of problems, it provides an explicit transformation of algorithms running in time $T$ that are only correct on a small (subconstant) fraction…

Growing context lengths in transformer-based language models have made the key-value (KV) cache a critical inference bottleneck. While many KV cache pruning methods have been proposed, they have not yet been adopted in major inference…

The discrete variables (DV) time-frequency (TF) quantum key distribution (QKD) protocol is a BB84 like protocol, which utilizes time and frequency as complementary bases. As orthogonal modulations, pulse position modulation (PPM) and…

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…

Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…

In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…

Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of…

We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different…

The Zap Q-learning algorithm introduced in this paper is an improvement of Watkins' original algorithm and recent competitors in several respects. It is a matrix-gain algorithm designed so that its asymptotic variance is optimal. Moreover,…

Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…

Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum…

It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial-LWE,…

Network quantization has proven to be a powerful approach to reduce the memory and computational demands of deep learning models for deployment on resource-constrained devices. However, traditional quantization methods often rely on access…

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give…