Related papers: Beyond Sparsity: Quantum Block Encoding for Dense …
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging problem. This paper presents a comprehensive study of the…
Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches…
Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
The cost of data input can dominate the run-time of quantum algorithms. Here, we consider data input of arithmetically structured matrices via block encoding circuits, the input model for the quantum singular value transform and related…
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
The parallel algorithm for loading large sparse matrices from files into distributed memories of high performance computing (HPC) systems is presented. This algorithm was designed specially for matrices stored in files in the space-effcient…