Related papers: Quantum walk approach to search on fractal structu…
Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks…
Quantum walk has been successfully used to search for targets on graphs with vertices identified as the elements of a database. This spacial search on a two-dimensional periodic grid takes $\mathcal{O}\left(\sqrt{N\log N}\right)$ oracle…
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
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…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
It was recently emphasized by Byrnes, Forster, and Tessler [Phys. Rev. Lett. 120, 060501 (2018)] that the continuous-time formulation of Grover's quantum search algorithm can be intuitively understood in terms of Rabi oscillations between…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…
Quantum walks have attracted attention as a promising platform realizing topological phenomena and many physicists have introduced various types of indices to characterize topologically protected bound states that are robust against…
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…
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…