Related papers: Quantum Algorithms for tensor-SVD
Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…
Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…
Continuous-variable (CV) quantum systems offer a natural framework for continuous optimization through their infinite-dimensional Hilbert spaces. In this paper, we propose the Complex Continuous-Variable Quantum Approximate Optimization…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…
Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…
Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Variational quantum algorithms (VQAs) provide a promising approach to achieving quantum advantage for practical problems on near-term noisy intermediate-scale quantum (NISQ) devices. Thus far, most studies on VQAs have focused on…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
Variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…
Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
Emerging quantum hardware provides new possibilities for quantum simulation. While much of the research has focused on simulating closed quantum systems, the real-world quantum systems are mostly open. Therefore, it is essential to develop…
This work presents a comprehensive overview of variational quantum computing and their key role in advancing quantum simulation. This work explores the simulation of quantum systems and sets itself apart from approaches centered on…
Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications,…