Related papers: On the Power of Quantum Algorithms for Vector Valu…
In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…
It has been shown that the apparent advantage of some quantum machine learning algorithms may be efficiently replicated using classical algorithms with suitable data access -- a process known as dequantization. Existing works on…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
We consider online algorithms with respect to the competitive ratio. Here, we investigate quantum and classical one-way automata with non-constant size of memory (streaming algorithms) as a model for online algorithms. We construct problems…
Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and, on the other hand, that such…
At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in…
While quantum architectures are still under development, when available, they will only be able to process quantum data when machine learning algorithms can only process numerical data. Therefore, in the issues of classification or…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…