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Acta Sinica Quantum Optica

Implementation of Grover Search Algorithm in 2-dimensional Photonic Crystals

Zhang Wen-hong

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Photonic crystal is a sort of artificial material,which has special characteristics.Recently,the application of photonic crystal in quantum computation has been introduced by Angelakis et al.In the paper,the implementation of the Grover search algorithm in two-dimensional planar photonic crystals for two-qubit system is proposed.By using the concepts of qubit and conditional quantum phase gate proposed by Angelakis et al,a more efficient and easily operated simulation of Grover algorithm is achieved.The details of scheme are given and related issues are discussed.

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Photonic crystal is a sort of artificial material,which has special characteristics.Recently,the application of photonic crystal in quantum computation has been introduced by Angelakis et al.In the paper,the implementation of the Grover search algorithm in two-dimensional planar photonic crystals for two-qubit system is proposed.By using the concepts of qubit and conditional quantum phase gate proposed by Angelakis et al,a more efficient and easily operated simulation of Grover algorithm is achieved.The details of scheme are given and related issues are discussed.
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.
The Grover quantum search algorithm is a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state marking scheme required to perform a classical search. We also report the deterministic implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.
This paper provides an introduction to a quantum search algorithm, known as Grover’s Algorithm, for unsorted search purposes. The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK by IBM. While providing detailed proof, the computational complexity of the algorithm is generalized to n qubits. The implementation results obtained from the IBM QASM Simulator and IBMQ Santiago quantum backend are analyzed and compared. Finally, the paper discusses the challenges faced in implementation and real-life applications of the algorithm hitherto. Overall, the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.
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.
Abstract We estimate the number of qubits on which the Grover search algorithm can be implemented in the framework of asynchronous atomic excitations in optical cavities. The main factor of decoherence is the broadening of spectral lines, following from the ‘‘time-energy’’ uncertainty relation and reveals in the photon transmission between cavities. The other factors of decoherence, issued from the scheme of entangling gate and the photon leak from the cavities, give the minor deposit. Our estimation shows that GSA can be fulfilled on no more than ten qubits through this scheme.