Related papers: A Unifying Framework for Doubling Algorithms
Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
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…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to additional applications of larger scale. We present a straightforward…
Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
In this paper we show how to construct diagonal scalings for arbitrary matrix pencils $\lambda B-A$, in which both $A$ and $B$ are complex matrices (square or nonsquare). The goal of such diagonal scalings is to "balance" in some sense the…
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
This paper is a continuation of \ct{cmf16} where an efficient algorithm for computing the maximal eigenpair was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements.…
Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the…
Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a…
Dearing and Zeck presented a dual algorithm for the problem of the minimum covering ball in $\mathbb{R}^n$. Each iteration of their algorithm has a computational complexity of at least $\mathcal O(n^3)$. In this paper we propose a…