Related papers: Spatial quantum search in a triangular network
We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers to efficiently address complex combinatorial optimization problems. Traditional Quantum Local Search…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic…
Quantum partial search algorithm is approximate search. It aims to find a target block (which has the target items). It runs a little faster than full Grover search. In this paper, we consider quantum partial search algorithm for multiple…
We report on an experiment on Grover's quantum search algorithm showing that {\em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed…
The Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to many areas in computer science and natural sciences. In this paper, we show that for the…
In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires…
A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a…
Quantum walk followed by some amplitude amplification technique has been successfully used to search for marked vertices on various graphs. Lackadaisical quantum walk can search for target vertices on graphs without the help of any…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
Quantum neural networks are promising for a wide range of applications in the Noisy Intermediate-Scale Quantum era. As such, there is an increasing demand for automatic quantum neural architecture search. We tackle this challenge by…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
Searching for an unknown marked vertex on a given graph (also known as spatial search) is an extensively discussed topic in the area of quantum algorithms, with a plethora of results based on different quantum walk models and targeting…