Related papers: Applications of the Adversary Method in Quantum Qu…
Artificial Intelligence has achieved remarkable success across diverse application domains. However, its vulnerability to adversarial attacks poses significant challenges to reliability, security, and trustworthiness. Adversarial machine…
The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted adversary…
We show that the quantum query complexity of detecting if an $n$-vertex graph contains a triangle is $O(n^{9/7})$. This improves the previous best algorithm of Belovs making $O(n^{35/27})$ queries. For the problem of determining if an…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.…
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…
We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known…
We present a quantum algorithm solving the $k$-distinctness problem in $O(n^{1-2^{k-2}/(2^k-1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$-query algorithm by Ambainis. The construction uses a modified…
In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…
As quantum computing continues to advance, the development of quantum-secure neural networks is crucial to prevent adversarial attacks. This paper proposes three quantum-secure design principles: (1) using post-quantum cryptography, (2)…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…
Adversarial attacks to graph analytics are gaining increased attention. To date, two lines of countermeasures have been proposed to resist various graph adversarial attacks from the perspectives of either graph per se or graph neural…
In this paper, we initiate the study of quantum algorithms in the Graph Drawing research area. We focus on two foundational drawing standards: 2-level drawings and book layouts. Concerning $2$-level drawings, we consider the problems of…
Graph neural networks, a popular class of models effective in a wide range of graph-based learning tasks, have been shown to be vulnerable to adversarial attacks. While the majority of the literature focuses on such vulnerability in…