Related papers: A Quantum Advantage for a Natural Streaming Proble…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
It is well known that for certain tasks, quantum computing outperforms classical computing. A growing number of contributions try to use this advantage in order to improve or extend classical machine learning algorithms by methods of…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
We prove that any two-pass graph streaming algorithm for the $s$-$t$ reachability problem in $n$-vertex directed graphs requires near-quadratic space of $n^{2-o(1)}$ bits. As a corollary, we also obtain near-quadratic space lower bounds for…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…
In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current…
Large-scale communication networks, such as the internet, rely on routing packets of data through multiple intermediate nodes to transmit information from a sender to a receiver. In this paper, we develop a model of a quantum communication…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
We present data streaming algorithms for the $k$-median problem in high-dimensional dynamic geometric data streams, i.e. streams allowing both insertions and deletions of points from a discrete Euclidean space $\{1, 2, \ldots \Delta\}^d$.…
We revisit the classic basic counting problem in the distributed streaming model that was studied by Gibbons and Tirthapura (GT). In the solution for maintaining an $(\epsilon,\delta)$-estimate, as what GT's method does, we make the…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
We initiate the study of the classical Submodular Cover (SC) problem in the data streaming model which we refer to as the Streaming Submodular Cover (SSC). We show that any single pass streaming algorithm using sublinear memory in the size…
In the past decade, the field of quantum machine learning has drawn significant attention due to the prospect of bringing genuine computational advantages to now widespread algorithmic methods. However, not all domains of machine learning…
The $\Sigma$-QMAC problem is introduced, involving $S$ servers, $K$ classical ($\mathbb{F}_d$) data streams, and $T$ independent quantum systems. Data stream ${\sf W}_k, k\in[K]$ is replicated at a subset of servers…
We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor $\alpha$ to be much larger than $1$. Such algorithms can use significantly less…