Related papers: Tensor Decompositions and Adiabatic Quantum Comput…

Quantum computing is developing fast. Real world applications are within reach in the coming years. One of the most promising areas is combinatorial optimisation, where the Quadratic Unconstrained Binary Optimisation (QUBO) problem…

Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

Quantum machine learning offers the ability to capture complex correlations in high-dimensional feature spaces, crucial for the challenge of detecting beyond the Standard Model physics in collider events, along with the potential for…

Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Hypergraph partitioning is a fundamental optimization problem with applications in data management and other domains involving higher-order relations. In this paper, we study balanced hypergraph partitioning from the perspective of quantum…

Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in…

Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…

Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…

Using Quantum Computers to solve problems in Recommender Systems that classical computers cannot address is a worthwhile research topic. In this paper, we use Quantum Annealers to address the feature selection problem in recommendation…

Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…

We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to…

We present a new method that efficiently solves TO problems and provides a practical pathway to leverage quantum computing to exploit potential quantum advantages. This work targets on large-scale, multi-material TO challenges for…

We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…