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Neutral atom technology has steadily demonstrated significant theoretical and experimental advancements, positioning itself as a front-runner platform for running quantum algorithms. One unique advantage of this technology lies in the…

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…

Quantum Physics · Physics 2023-09-19 Changpeng Shao

It is proved that there exist graphs of bounded degree with arbitrarily large queue-number. In particular, for all $\Delta\geq3$ and for all sufficiently large $n$, there is a simple $\Delta$-regular $n$-vertex graph with queue-number at…

Combinatorics · Mathematics 2008-09-09 David R. Wood

Training and inference with large machine learning models that far exceed the memory capacity of individual devices necessitates the design of distributed architectures, forcing one to contend with communication constraints. We present a…

Quantum Physics · Physics 2024-09-30 Dar Gilboa , Hagay Michaeli , Daniel Soudry , Jarrod R. McClean

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

Combinatorics · Mathematics 2013-11-13 Svante Janson , Simone Severini

An ordered graph is a graph together with a linear order on its vertices. A hereditary property of ordered graphs is a collection of ordered graphs closed under taking induced ordered subgraphs. If P is a property of ordered graphs, then…

Combinatorics · Mathematics 2007-05-23 József Balogh , Béla Bollobás , Robert Morris

Quantum advantage is well-established in centralized computing, where quantum algorithms can solve certain problems exponentially faster than classical ones. In the distributed setting, significant progress has been made in…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-03-17 Francesco d'Amore

We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…

Quantum Physics · Physics 2020-08-19 Juan Miguel Arrazola , Alain Delgado , Bhaskar Roy Bardhan , Seth Lloyd

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…

Quantum Physics · Physics 2025-11-04 Nhat A. Nghiem

We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…

Computational Complexity · Computer Science 2007-05-23 H. Buhrman , R. Cleve , R. de Wolf , Ch. Zalka

We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and…

Quantum Physics · Physics 2026-04-01 Thomas Huffstutler , Upendra Kapshikar , David Miloschewsky , Supartha Podder

In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…

Data Structures and Algorithms · Computer Science 2017-06-29 Caishi Fang

The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…

Establishing quantum speedup for computationally hard problems of practical relevance, particularly combinatorial optimization problems, remains a central challenge in quantum computation. In this work, we identify a structurally defined…

Quantum Physics · Physics 2026-01-27 Vicky Choi

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

Dynamical Systems · Mathematics 2018-07-26 Delio Mugnolo

Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…

Discrete Mathematics · Computer Science 2021-11-04 Pablo Arrighi , Simon Martiel

One of the most fundamental questions in graph property testing is to characterize the combinatorial structure of properties that are testable with a constant number of queries. We work towards an answer to this question for the…

Data Structures and Algorithms · Computer Science 2018-11-08 Hendrik Fichtenberger , Pan Peng , Christian Sohler

Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…

Combinatorics · Mathematics 2009-07-02 Gabor Elek

Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a…

Discrete Mathematics · Computer Science 2020-12-03 Daniel Chen , Yekun Xu , Betis Baheri , Samuel A. Stein , Chuan Bi , Ying Mao , Qiang Quan , Shuai Xu

Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…

Quantum Physics · Physics 2024-11-07 Jason Pollack , Dylan VanAllen