Related papers: Beyond Sparsity: Quantum Block Encoding for Dense …
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
This paper seeks to combine dictionary learning and hierarchical image representation in a principled way. To make dictionary atoms capturing additional information from extended receptive fields and attain improved descriptive capacity, we…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
In an iterative approach for solving linear systems with ill-conditioned, symmetric positive definite (SPD) kernel matrices, both fast matrix-vector products and fast preconditioning operations are required. Fast (linear-scaling)…
We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder…
Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been…
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…
Embedding image features into a binary Hamming space can improve both the speed and accuracy of large-scale query-by-example image retrieval systems. Supervised hashing aims to map the original features to compact binary codes in a manner…
Factorization of large dense matrices are ubiquitous in engineering and data science applications, e.g. preconditioners for iterative boundary integral solvers, frontal matrices in sparse multifrontal solvers, and computing the determinant…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
Large-scale machine learning (ML) models are increasingly being used in critical domains like education, lending, recruitment, healthcare, criminal justice, etc. However, the training, deployment, and utilization of these models demand…