Entanglement lies at the heart of quantum mechanics and has no classical analogue. It is central to the speed up achieved by quantum algorithms over their classical counterparts. The Grover’s search algorithm is one such algorithm which enables us to achieve a quadratic speed up over any known classical algorithm that searches for an element in an unstructured database. Here, we analyse and qua...

This paper presents an original Quantum Genetic algorithm for Multiple sequence ALIGNment (QGMALIGN) that combines a genetic algorithm and a quantum algorithm. A quantum probabilistic coding is designed for representing the multiple sequence alignment. A quantum rotation gate as a mutation operator is used to guide the quantum state evolution. Six genetic operators are designed on the coding ba...

Grover's quantum search algorithm has recently been implemented without entanglement, by replacing multiple particles with a single particle having exponentially many states. We recall that all physical resources must be accounted for to quantify algorithm complexity, and that this scheme typically incurs exponential costs in some other resource(s). In particular, we demonstrate that a recent e...

This paper proves lower bounds of the quantum query complexity of a multiple-block ordered search problem, which is a natural generalization of the ordered search problems. Apart from much studied polynomial and adversary methods for quantum query complexity lower bounds, our proof employs an argument that (i) commences with the faulty assumption that a quantum algorithm of low query complexity...

In this paper, we present a new framework for combining complete and incomplete methods in order to deal with the Max Sat problem. The objective is to find the best assignment for a set of Boolean variables, which gives the maximum of verified clauses in a Boolean formula. Unfortunately, this problem has been shown to be NP-hard (non-deterministic polynomial-time hard) if the number of variable...

This paper proves lower bounds of the quantum query complexity of a multiple-block ordered search problem, which is a natural generalization of the ordered search problems. Apart from much studied polynomial and adversary methods for quantum query complexity lower bounds, our proof employs an argument that (i) commences with the faulty assumption that a quantum algorithm of low query complexity...

There are hamiltonians that solve a search problem of finding one of N items in O( √ N) steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, Hg. Then the known search hamiltonians become special cases of Hg. From the generalized search hamiltonian, we present remarkable results that searching with 100% is subject ...

In the future quantum computers may allow us to process information in ways not possible on classical computers. The invention of algorithms to run on a quantum computer is a very difficult task, a fact made evident by the small number of algorithms currently known. This essay is intended as a review of the most important quantum algorithms, and will hopefully allow the reader to gain some unde...

Riding a different wave: This study shows that an acoustic metasurface can be platform to implement airborne surface waves (SAWs) for analog computing based on quantum algorithm. The authors' gradient-index system used perform the Grover search algorithm, with quadratic speedup over classical searches. Such SAW-based would offer---in foreseeable future---a flexible simulation of algorithms, whi...