Related papers: Decomposing dense matrices into dense Pauli tensor…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The…
Decomposing Pauli exponentials efficiently to quantum circuits has been the subject of intense research in recent years. Pauli exponentials are an essential component of many different quantum algorithms. Due to the error-prone nature of…
Sparse tensors are the most used representation of sparse multidimensional data. Operations that decompose them, selecting their most important features while reducing their dimension, have become prevalent procedures in machine learning.…
We introduce a coefficient-decoupled matrix product operator (MPO) representation for Pauli-sum operators that separates reusable symbolic operator support from a tunable coefficient bridge across a fixed bipartition. This representation…
We present a spatially efficient decomposition of matrices and arbitrary-order tensors as linear combinations of tensor products of $\{-1, 1\}$-valued vectors. For any matrix $A \in \mathbb{R}^{m \times n}$, $$A - R_w = S_w C_w T_w^\top =…
A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
We give the first two algorithms to enumerate all binary words of $\{0,1\}^\ell$ (like Gray codes) while ensuring that the delay and the auxiliary space is independent from $\ell$, i.e., constant time for each word, and constant memory in…
Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. When this set is taken to consist of only products of Pauli operators, we show that the minimal such set generating…
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…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
In this paper we describe a heuristic for decomposing a directed graph into factors according to the direct product (also known as Kronecker, cardinal or tensor product). Given a directed, unweighted graph~$G$ with adjacency matrix…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…