Related papers: Quantum search algorithms on a regular lattice
Although entanglement is widely considered to be necessary for quantum algorithms to improve on classical ones, Lloyd has observed recently that Grover's quantum search algorithm can be implemented without entanglement, by replacing…
We present various results on the scheme introduced , which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field…
Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…
We study the average probability that a discrete-time quantum walk finds a marked vertex on a graph. We first show that, for a regular graph, the spectrum of the transition matrix is determined by the weighted adjacency matrix of an…
The lazy random walk, where the walker has some probability of staying put, is a useful tool in classical algorithms. We propose a quantum analogue, the lackadaisical quantum walk, where each vertex is given $l$ self-loops, and we…
The lecture notes contain three parts. The first part is Grover's Search Algorithm with modifications, generalizations, and applications. The second part is a discussion on the quantum fingerprinting technique. The third part is Quantum…
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject…
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…
We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap.…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
We present quantum algorithms to search for marked vertices in structured databases with low connectivity. Adopting a multi-stage search process, we achieve a success probability close to $100\%$ on Cayley trees with large branching…
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical…