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IEEE Transactions on Circuits and Systems I Regular Papers

Quantum Circuit Design and Analysis for Database Search Applications

Yi-Lin Ju, I-Ming Tsai, Sy‐Yen Kuo

Published Nov 1, 2007• 27 citations
Publisher

Abstract

In this paper, we show how quantum Boolean circuits can be used to implement the oracle and the inversion-about-average function in Grover's search algorithm. Before illustrating how this can be done, we present the circuit design principle using the satisfiability (SAT) problem as an example. Then, based on this principle, we show the quantum circuits for two different kinds of applications. The first one is searching a phone book. Although this is a typical example of Grover's algorithm, we show that it is impractical as a real-world application. As the second application, we give the quantum circuits for a more practical application-breaking a symmetric cryptosystem. Although these two applications have quite different types of search criteria, they are both one-way functions and the proposed circuits can actually be generalized to any such problems. In this perspective, we conclude this paper by proposing a template of quantum circuits that is capable of searching the solution of a certain class of one-way functions.

DOI
10.1109/tcsi.2007.907845

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In this paper, we show how quantum Boolean circuits can be used to implement the oracle and the inversion-about-average function in Grover's search algorithm. Before illustrating how this can be done, we present the circuit design principle using the satisfiability (SAT) problem as an example. Then, based on this principle, we show the quantum circuits for two different kinds of applications. The first one is searching a phone book. Although this is a typical example of Grover's algorithm, we show that it is impractical as a real-world application. As the second application, we give the quantum circuits for a more practical application-breaking a symmetric cryptosystem. Although these two applications have quite different types of search criteria, they are both one-way functions and the proposed circuits can actually be generalized to any such problems. In this perspective, we conclude this paper by proposing a template of quantum circuits that is capable of searching the solution of a certain class of one-way functions.
The discovery of polynomial time prime factorization, secure key distribution, and fast database search algorithm have recently made quantum computing the most rapidly expanding research field. For a quantum algorithm to be useful, it is essential that the algorithm can be implemented using quantum circuits. Nanotechnology, in particular quantum mechanics based devices, can be used to realize such an algorithm. In this paper, we show how quantum Boolean circuits can be used to implement the oracle circuit and the inversion-about-average function in Grover's search algorithm. We also show that a slight modification of the oracle circuit can be used to search multiple targets.
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical algorithm. It is possible to use Grover algorithm, taking profit of its ability to find a specific value in a unordered database, to find, for example, the zero of a logical function; the minimal or maximal value in a database or to recognize if an odd number is prime or not. Here we show quantum algorithms to solve those cited mathematical problems. The solution requires the use of a quantum bit string comparator being used as oracle. This quantum circuit compares two quantum states and identifies if they are equal or, otherwise, which of them is the largest. Moreover, we also show the quantum bit string comparator allow us to implement conditional statements in quantum computation, a fundamental structure for designing of algorithms.
Quantum computing has become an important research field of computer science and engineering. Among many quantum algorithms, Grover's algorithm is one of the most famous ones. Designing an effective quantum oracle poses a challenging conundrum in circuit and system-level design for practical application realization of Grover's algorithm. In this dissertation, we present a new method to build quantum oracles for Grover's algorithm to solve graph theory problems. We explore generalized Boolean symmetric functions with lattice diagrams to develop a low quantum cost and area efficient quantum oracle. We study two graph theory problems: cycle detection of undirected graphs and generalized hypercube partitioning. We present a novel method to design a quantum oracle to solve Boolean function minimization problems which occur in classical circuit optimization.
This study investigates the application of quantum computing to the Boolean satisfaction problem (SAT), with a special focus on the special case of the Exactly-1 3-SAT problem. Quantum computing has shown significant advantages in solving various computational problems and achieving exponential accelerations. This study designs and implements a quantum algorithm to identify assignments that prove Boolean formulas of bound form using the Grover search algorithm. We tested the implementation of three quantum circuits using as many quantum techniques as possible using the IBM quantum simulator. Only the second implementation showed consistent results due to the number of qubits, decoherence time, and circuit complexity. This study demonstrates that the design of algorithms meets hardware constraints and lays the foundation for future research as quantum devices improve.
The search for information in a system has been a continuous problem for a computer. This has resulted in the construction of a set of classical algorithms that can search for a set of data. This is why search systems can be divided into the type of information being searched, the number of solutions to find, and even the terms used for searching. With the emergence of quantum computing, new algorithms have been generated for this type of process. An example is the Grover algorithm, which performs theoretically better than traditional algorithms. This is why there has been research on optimizing it, applying it to new fields, and making it more accessible to industry users. Even if the algorithm is a promising alternative, one of the disadvantages of Grover’s algorithm is the use of an oracle function that must be generated for every set of search data. This review describes three sets of methodologies for generating quantum circuits that can be applied to constructing this oracle quantum circuit.
The main idea in the original Grover search (1997 Phys. Rev. Lett. 79 325) is to single out a target state containing the solution to a search problem by amplifying the amplitude of the state, following the Oracle's job, i.e., a black box giving us information about the target state. We design quantum circuits to accomplish a complete Grover search involving both the Oracle's job and the amplification of the target state, which are employed to solve satisfiability (SAT) problems. We explore how to carry out the quantum circuits with currently available ion-trap quantum computing technology.