Related papers: Quantum Kaczmarz Algorithm for Solving Linear Alge…
We develop a quantum algorithm for linear algebraic equations $ A\bb{x} = \bb{b} $ from the perspective of Schr\"odingerization-form problems, which are characterized by a system of linear convection equations in one higher dimension. When…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
We consider the task of estimating the expectation value of an $n$-qubit tensor product observable $O_1\otimes O_2\otimes \cdots \otimes O_n$ in the output state of a shallow quantum circuit. This task is a cornerstone of variational…
Finding a Hadamard matrix of a specific order using a quantum computer can lead to a demonstration of practical quantum advantage. Earlier efforts using a quantum annealer were impeded by the limitations of the present quantum resource and…
Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim and Lloyd for solving systems of linear equations. The utility of {classical} linear…
Existing quantum discrete adiabatic approaches are hindered by circuit depth that increases linearly with the number of evolution steps, a significant challenge for current quantum hardware with limited coherence times. To address this, we…
The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin…
To exploit the benefits of massive multiple-input multiple-output (M-MIMO) technology in scenarios where base stations (BSs) need to be cheap and equipped with simple hardware, the computational complexity of classical signal processing…
Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
We describe a fast solver for linear systems with reconstructable Cauchy-like structure, which requires O(rn^2) floating point operations and O(rn) memory locations, where n is the size of the matrix and r its displacement rank. The solver…
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…