Related papers: Quantum Database Search can do without Sorting

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…

Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…

We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…

We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…

Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum…

In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…

This paper gives a simple proof of why a quantum computer, despite being in all possible states simultaneously, needs at least 0.707 sqrt(N) queries to retrieve a desired item from an unsorted list of items. The proof is refined to show…

Drug discovery has become a main challenge in our society, following the Covid-19 pandemic. Even pharmaceutical companies are already using computing to accelerate drug discovery. They are increasingly interested in Quantum Computing with a…

This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…

Composition is something we take for granted in classical algorithms design, and in particular, we take it as a basic axiom that composing ``efficient'' algorithms should result in an ``efficient'' algorithm -- even using this intuition to…

Many text databases on the web are "hidden" behind search interfaces, and their documents are only accessible through querying. Search engines typically ignore the contents of such search-only databases. Recently, Yahoo-like directories…

Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…

Keyword search against structured databases has become a popular topic of investigation, since many users find structured queries too hard to express, and enjoy the freedom of a ``Google-like'' query box into which search terms can be…

Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…

Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…

We explore the collapse of "wavefunction" and the measurement of entanglement in the superpositions of hyperspace vectors in classical physical instantaneous-noise-based logic (INBL). We find both similarities with and major differences…

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…

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…