Related papers: Improved Classical and Quantum Algorithms for the …
Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless…
In the present paper we study a non-modular variant of the Short Integer Solution problem over the integers. Given a random matrix $A \in \mathbb{Z}^{n\times m}$ with entries $a_{ij}$ such that $0\le a_{ij}< Q,$ for some $Q>0,$ the goal is…
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…
One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…
Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…
In the decremental single-source shortest paths (SSSP) problem, the input is an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges undergoing edge deletions, together with a fixed source vertex $s\in V$. The goal is to maintain a…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a…
Hundreds of satellites equipped with cameras orbit the Earth to capture images from locations for various purposes. Since the field of view of the cameras is usually very narrow, the optics have to be adjusted and rotated between single…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We propose a unified framework that synthesizes advances in high-dimensional lattice theory with novel computational algorithms for the shortest vector problem (SVP) to model pure root lattices and compute sphere packing densities. Building…
A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…
Motivated by the quantum speedup for dynamic programming on the Boolean hypercube by Ambainis et al. (2019), we investigate which graphs admit a similar quantum advantage. In this paper, we examine a generalization of the Boolean hypercube…
Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…