Related papers: A Time-Efficient Output-Sensitive Quantum Algorith…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves…
The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…
We study the problem of determining the Boolean product of two n\times n Boolean matrices in an unconventional computational model allowing for mechanical operations. We show that O(n^2) operations are sufficient to compute the product in…
We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in $\hat{O}(n^3/\log^4 n)$ time, where the $\hat{O}$ notation suppresses poly(loglog) factors. This improves the previous best…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
We study the problem of multiplying two bit matrices with entries either over the Boolean algebra $(0,1,\vee,\wedge)$ or over the binary field $(0,1,+,\cdot)$. We engineer high-performance open-source algorithm implementations for…
We consider the problem of doing fast and reliable estimation of the number of non-zero entries in a sparse boolean matrix product. This problem has applications in databases and computer algebra. Let n denote the total number of non-zero…
We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different…
Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained reductions, we investigate the question whether the multiplication of two $n\times n$ matrices can be performed in near-optimal…
Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…
We consider the Online Boolean Matrix-Vector Multiplication (OMV) problem studied by Henzinger et al. [STOC'15]: given an $n \times n$ Boolean matrix $M$, we receive $n$ Boolean vectors $v_1,\ldots,v_n$ one at a time, and are required to…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…