Related papers: Deterministic quantum search on all Laplacian inte…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
Since quantum spatial searches on complex networks have a strong network dependence, the question arises whether the universal perspective exists in this quantum algorithm for complex networks. Here, we uncover the universal scaling laws of…
This paper deals with the problem of the requirements for quantum systems that enable one to design efficient quantum algorithms. We rise the issue of the possibility to utilise the non-complete networks for algorithmic purposes. In…
We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…
The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by…
The diagonal entries of pseudoinverse of the Laplacian matrix of a graph appear in many important practical applications, since they contain much information of the graph and many relevant quantities can be expressed in terms of them, such…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian,…
We consider the quantum search problem with a continuous time quantum walk for networks of finite spectral dimension d_{s} of the network Laplacian. For general networks of fractal (integer or non-integer) dimension d_{f}, for which in…
This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the World Wide Web in classical computation. From a broader…
Quantum walks provide a powerful framework for achieving algorithmic speedup in quantum computing. This paper presents a quantum search algorithm for 2-tessellable graphs, a generalization of bipartite graphs, achieving a quadratic speedup…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$.…
A single excitation in a quantum spin network described by the Heisenberg model can effect a variety of continuous-time quantum walks on unweighted graphs, including those governed by the discrete Laplacian, adjacency matrix, and signless…
The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on…
Given $x, y$ on an unweighted undirected graph $G$, the goal of the pathfinding problem is to find an $x$-$y$ path. In this work, we first construct a graph $G$ based on welded trees and define a pathfinding problem in the adjacency list…
In the paper, we consider the problem of searching for the Largest empty rectangle in a 2D map, and the one-dimensional version of the problem is the problem of searching for the largest empty segment. We present a quantum algorithm for the…
Given an item and a list of values of size $N$. It is required to decide if such item exists in the list. Classical computer can search for the item in O(N). The best known quantum algorithm can do the job in $O(\sqrt{N})$. In this paper, a…