Related papers: Spatial quantum search in a triangular network
Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
All-sky, broadband, coherent searches for gravitational-wave pulsars are restricted by limited computational resources. Minimizing the number of templates required to cover the search parameter space, of sky position and frequency…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…
Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a…
In the SEARCH WITH ADVICE problem, a single entry of interest within a database of N entries is to be found assuming that an ordering of the entries, from that with the highest probability of being the entry of interest (as determined by a…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…
Quantum search algorithms are crucial for exploring large solution spaces, but their robustness to environmental perturbations, such as noise or disorder, remains a critical challenge. We examine the impact of biased disorder potentials…
Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…
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…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
Quantum query complexity is typically characterized in terms of XOR queries |x,y> to |x,y+f(x)> or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is…
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
Given two sets A and B and two oracles O(A) and O(B) that can identify the elements of these sets respectively, the goal is to find an element common to both sets using minimum number of oracle queries. Each application of either O(A) or…
Since Grover's seminal work which provides a way to speed up combinatorial search, quantum search has been studied in great detail. We propose a new method for designing quantum search algorithms for finding a marked element in the state…
Unlike classical routing algorithms, quantum routing algorithms make use of entangled states - a type of resources that have a limited lifetime and need to be regenerated after consumption. In a nutshell, quantum routing algorithms have to…
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…