Related papers: Improved quantum lower and upper bounds for matrix…
Classical algorithms for market equilibrium computation such as proportional response dynamics face scalability issues with Internet-based applications such as auctions, recommender systems, and fair division, despite having an almost…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
We study possible advantages of randomized and quantum computing over deterministic computing for scalar initial-value problems for ordinary differential equations of order k. For systems of equations of the first order this question has…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
We give a classical analogue to Kerenidis and Prakash's quantum recommendation system, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning. Our main result is an algorithm…
Mixed Integer Programs (MIPs) model many optimization problems of interest in Computer Science, Operations Research, and Financial Engineering. Solving MIPs is NP-Hard in general, but several solvers have found success in obtaining…
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…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
It is shown that quantum computer can detect the existence of root of a function almost exponentially more efficient than the classical counterpart. It is also shown that a quantum computer can produce quantum state corresponding to the…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…