Related papers: A general quantum matrix exponential dimensionalit…

As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…

The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is extended to constrained optimization problems, establishing conditions for equivalence between the solution and constraints. A dual formulation of…

We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors…

A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an…

Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…

We examine the challenges associated with numerical integration when applying Neural Networks to solve Partial Differential Equations (PDEs). We specifically investigate the Deep Ritz Method (DRM), chosen for its practical applicability and…

Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency,…

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…

Block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In…

In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…

We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture…

Many recent works on Entity Resolution (ER) leverage Deep Learning techniques involving language models to improve effectiveness. This is applied to both main steps of ER, i.e., blocking and matching. Several pre-trained embeddings have…

Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large…

Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex…

Empirical risk minimization (ERM) and distributionally robust optimization (DRO) are popular approaches for solving stochastic optimization problems that appear in operations management and machine learning. Existing generalization error…

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…

Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…

Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…

This study tackles the computational challenges of solving Markov Decision Processes (MDPs) for a restricted class of problems. It is motivated by the Last Revealer Attack (LRA), which undermines fairness in some Proof-of-Stake (PoS)…