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Journal of Physics Conference Series

Theoretical research of the distortion of quantum circuit in Grover's algorithm

Kseniya Gubaidullina, Sergey A. Chivilikhin

Published Aug 1, 2016• 2 citations
Publisher

Abstract

Grover's algorithm is a quantum search algorithm among unsorted elements that can do several operations at the same time due to their wave like properties. In addition, it could solve problems of global optimization and graph coloring. This work presents the results of the simulation of Grover's algorithm and research of its resistance to the effects of perturbations of quantum logic circuit elements. These dependencies can be useful for creating optical circuit.

DOI
10.1088/1742-6596/735/1/012074

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Grover's algorithm is a quantum search algorithm among unsorted elements that can do several operations at the same time due to their wave like properties. In addition, it could solve problems of global optimization and graph coloring. This work presents the results of the simulation of Grover's algorithm and research of its resistance to the effects of perturbations of quantum logic circuit elements. These dependencies can be useful for creating optical circuit.
Grover's algorithm is a quantum algorithm for searching specified elements in an unsorted list.It has many valuable applications.The utilization of Grover's algorithm, to adapt it to accelerate the works of well-known classical algorithms, is very promising, and it is one of the fastest algorithms to solve such problems like global optimization and graph coloring.In this regard, it is very important to study the stability of the Grover's algorithm, to know how distortion of the circuit's elements affects on it results.This work presents the results of the simulation of Grover's algorithm, research of its stability with respect to perturbations of quantum logic circuit elements and its dependencies from the number of qubits, used in quantum circuit.Another part of this research was realized on IBM quantum processor and shows the stability of the 2-qubit Grover's algorithm.
Grover’s algorithm is a quantum search algorithm that makes a huge difference in finding an element of interest from unsorted and unstructured data. In the case of a classical search algorithm, testing O(N) elements within a dataset of size N is a significant number. Grover’s algorithm reduces this number to O(N)O(\sqrt N )O(N​) so the gain is obvious. This paper covers applied aspects of Grover’s algorithm, namely quantum circuit layout, efficiency of gates, fidelity of qubits, and the optimization of resources for searching unstructured data. Focus has been placed on quantum error correction: namely, planar surface code; resource costs involved have been quantified. The paper discusses the implications of quantum computing on data retrieval and how algorithms in quantum computing are crucial for solving issues presented by a changing environment of computation.
We observe an enormous increase in the computational power of digital computers. This was due to the revolution in manufacturing processes and controlling semiconductor structures on submicron scale, ultimately leading to the control of individual atoms. Eventually, the classical electric circuits encountered the barrier of quantum mechanics and its effects. However, the laws of quantum mechanics can be also used to produce computational devices that lead to extraordinary speed increases over classical computers. Thus quantum computing becomes a very promising and attractive research area. The Computer Aided Design for Quantum circuits becomes an essential ingredient for such emerging research which may lead to these powerful computers to be realized—an era of Quantum computing. This thesis presents an integrated theoretical study of software algorithms to design circuits of quantum oracles as well as methods for designing quantum oracles for Grover algorithm to solve combinatorial problems. An implementation of quantum algorithm involves the initialization of the input state and its manipulation with quantum gates followed by the measurements. In Grover algorithm the problem to be solved is specified by a permutative logic oracle – the fundamental problem is then how to build this oracle from quantum logic circuits and how to optimize these circuits. These problems are NP-hard and require search algorithms. In future, the search will be also done in quantum and this thesis leads to quantum algorithms to design quantum circuits more efficiently.
A quantum computation problem of quantum search is discussed in this paper.Grover's search algorithm, the most commonly used quantum search algorithm, is introduced in details.The flow of quantum search algorithm and the quantum circuit model are shown.And the error of the search value, as well as the probability of measurement, is analyzed.For further research we simulated the Grover's search algorithm in classical computer.By quantum simulator the probability distribution of the measuring result of search value is presented and the computational efficiency is discussed.The simulation result demonstrates the effectiveness of the proposed algorithm.
Many applications such as Graph coloring, Triangle finding, Boolean satisfiability, Traveling salesman problem can be solved by Grover's search algorithm, which is one of the remarkable quantum computing algorithm. To design a quantum circuit for a given quantum algorithm, which involves Grover's search, we need to define an oracle circuit specific to the given algorithm and the diffusion operator for amplification of the desired quantum state. In this paper, we propose a quantum circuit implementation for the oracle of the vertex coloring problem based on Grover's algorithmic approach. To the best of our knowledge, this is a first of its kind approach in regards to the quantum circuit synthesis of the vertex coloring oracle in binary quantum domain. We have performed the synthesis of the proposed oracle circuit for the six commonly available Physical Machine Description (PMD) gate libraries using the Fault Tolerant Quantum Logic Synthesis (FTQLS) tool. The synthesis results have been presented to understand the cost estimation of the oracle circuit for the various PMDs in terms of number of quantum operations and number of cycles.
At present, the scale of quantum computers in the real sense is still small, and quantum simulation has become one of the important ways of quantum theory research, grover quantum search algorithm is suitable for the search problem of disordered database. Firstly, according to the implementation principle of Grover algorithm and Boolean logic relationship, the design idea of multi-objective Oracle is analyzed, based on IBMQ quantum cloud platform, the quantum circuit of Grover algorithm with multi-objective items is simulated. Based on the characteristics of Grover algorithm and the simulation process of quantum gate, the action of multiple identical quantum gates is combined to reduce the update times of probability amplitude and improve the simulation efficiency. The libquantum quantum simulator is used for experiments and the target item is successfully searched, which proves the feasibility of the optimization method and provides reference for the simulation and optimization of other quantum algorithms.