Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The amount of quantum memory required is $O(N^{1/2})$. The quantum algorithm that accomplishes this consists of an inner Grover search combined with a partial sort all sitting inside of an outer Grover search.
Given $κ$ databases of unstructured entries, we propose a quantum algorithm to find the common entries between those databases. The proposed algorithm requires $\mathcal{O}(κ\sqrt{N})$ queries to find the common entries, where $N$ is the number of records for each database. The proposed algorithm constructs an oracle to mark common entries, and then uses a variation of amplitude amplification technique with reliable behavior to increase the success probability of finding them.
Manipulating a database system on a quantum computer is an essential aim to benefit from the promising speed-up of quantum computers over classical computers in areas that take a vast amount of storage and processing time such as in databases. In this paper, the basic operations for manipulating the data in a quantum database will be defined, e.g. INSERT, UPDATE, DELETE, SELECT, backing up and restoring a database file. This gives the ability to perform the data processing that usually takes a long processing time on a classical database system, in a simultaneous way on a quantum computer. Def…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database has to return a (YES/NO) answer). A classical algorithm will be limited to the information theoretic bound of at least O(log N) queries (which it would achieve by using a binary search).
Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to spe…
Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.
In this summary we discuss two new algorithms for Grover's unsorted database search problem that claimed to have reached exponential speedup over Grover's original algorithm. One is in the quantum setting with "power queries" that allow for exponential reduction in the number of queries over Grover's original algorithm with "bit queries". The other is to use "dubit queries" on a duality computer - a new computing model uses a quantum system's wave-particle duality, which is able to achieve even greater computing power and better capability than existent quantum computers we have been discussin…
The approach given by Grover can be generalised to set an upper complexity limit to the basic operations of relational algebra on a quantum computer. Except in special cases where indices can be used on a classical machine, the quantum upper complexity limit is lower than the classical one.
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 database with quadratic speedup over the best known classical algorithm. This review paper discusses the performance of Grover's algorithm in case of multiple matches where the problem is expected to be easier. Unfortunately, we will find that the algorithm will fail for $M>3N/4$, where $M$ is the number of matches in the list.
Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical counterpart for implementing the main task of ARM, i.e., finding frequent itemsets from a transaction database. In this paper, we experimentally implement qARM on both real quantum computers and a quantum computing simulator via the IBM quantum computing platform. In the first place, we design quantum circuits of qARM for a 2$\times$2 transaction database (i.e., a transaction data…
A Quantum Computer is a new type of computer which can solve problems such as factoring and database search very efficiently. The usefulness of a quantum computer is limited by the effect of two different types of errors, decoherence and inaccuracies. In this paper we show the results of simulations of a quantum computer which consider both decoherence and inaccuracies. We simulate circuits which factor the numbers 15, 21, 35, and 57 as well as circuits which use database search to solve the circuit satisfaction problem. Our simulations show that the error rate per gate is on the order of 10^-…
In a recent paper (quant-ph/0506105), A S Gupta, M. Gupta and A. Pathak proposed a modified Grover algorithm that would exponentially accelerate the unsorted database search problem if the number of marked items is known. If this were true, it would represent a major fundamental breakthrough in computer science, mathematics, quantum information and other related branches of sciences. However the algorithm is not valid. We will explain it in this brief comment.
We describe a quantum computer emulator for a generic, general purpose quantum computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch-Jozsa and Grover's database search algorithm.
The conventional protection of information by cryptographical keys makes no sense if a key can be quickly discovered by an unauthorized person. This way of penetration to the protected systems was made possible by a quantum computers in view of results of P.Shor and L.Grover. This work presents the method of protection of an information in a database from a spy even he knows all about its control system and has a quantum computer, whereas a database can not distinguish between operations of spy and legal user.
An important and usual problem is to search all states we want from a database with a large number of states. In such, recall is vital. Grover's original quantum search algorithm has been generalized to the case of multiple solutions, but no one has calculated the query complexity in this case. We will use a generalized algorithm with higher precision to solve such a search problem that we should find all marked states and show that the practical query complexity increases with the number of marked states. In the end we will introduce an algorithm for the problem on a ``duality computer'' and …
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyze the difficulties that are encountered in programming physical realizations of quantum computers. Examples of logically identical implementations of the controlled-NOT operation and Grover's database search algorithm are used to demonstrate that the results of a quantum computation are unstable with respect to the physical realization of the quantum computer. We discuss the origin of these instabilities and discuss possibili…
We show how to perform a quantum search for a classical object, specifically for a classical object which performs no coherent evolution on the quantum computer being used for the search. We do so by using interaction free measurement as a subroutine in a quantum search algorithm. In addition to providing a simple example of how non-unitary processes which approximate unitary ones can be useful in a quantum algorithm, our procedure requires only one photon regardless of the size of the database, thereby establishing an upper bound on the amount of energy required to search an arbitrarily large…
We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some preliminary results on the stability of quantum algorithms are presented.
The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves th…
Proposed below is a reversible digital computer modeled after the natural behavior of a quantum system. Using approaches usually reserved for idealized quantum computers, the Reversible CAM, or State Vector Parallel (RSVP) processor can easily find keywords in an unstructured database (that is, it can solve a needle in a haystack problem). The RSVP processor efficiently solves a SAT (Satisfiability of Boolean Formulae) problem; also it can aid in the solution of a GP (Global Properties of Truth Table) problem. The power delay product of the RSVP processor is exponentially lower than that of a …
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report res…
