Related papers: Parameterized Quantum Query Algorithms for Graph P…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters…
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…
Given a graph, a $k$-plex is a set of vertices in which each vertex is not adjacent to at most $k-1$ other vertices in the set. The maximum $k$-plex problem, which asks for the largest $k$-plex from the given graph, is an important but…
Methods for query answering over incomplete knowledge graphs retrieve entities that are likely to be answers, which is particularly useful when such answers cannot be reached by direct graph traversal due to missing edges. However, existing…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
In the vertex cover problem, the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every edge of $G$ is incident on at least one vertex in $S$. We study…
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…
Nowadays in Quantum Computing, the implementation of quantum algorithm has created a stir since Noisy Intermediate-Scale Quantum (NISQ) devices are out in the market. Researchers are mostly interested in solving NP-complete problems with…
We study a recently introduced generalization of the Vertex Cover (VC) problem, called Power Vertex Cover (PVC). In this problem, each edge of the input graph is supplied with a positive integer demand. A solution is an assignment of…
Let $H$ be a fixed graph on $n$ vertices. Let $f_H(G) = 1$ iff the input graph $G$ on $n$ vertices contains $H$ as a (not necessarily induced) subgraph. Let $\alpha_H$ denote the cardinality of a maximum independent set of $H$. In this…
In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area:…
Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012] introduced the Anchored k-Core problem, where the task is for a given graph G and integers b, k, and p to find an induced subgraph H with at least p vertices (the core) such…
The survey provides an overview of the developing area of parameterized algorithms for graph modification problems. We concentrate on edge modification problems, where the task is to change a small number of adjacencies in a graph in order…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Performance of cryptanalytic quantum search algorithms is mainly inferred from query complexity which hides overhead induced by an implementation. To shed light on quantitative complexity analysis removing hidden factors, we provide a…