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Advances in intelligent systems and computing

An Introduction to Quantum Search Algorithm and Its Implementation

Jose P. Dumas, Kapil Kumar Soni, Akhtar Rasool

Published Aug 9, 2018• 1 citation
Publisher
DOI
10.1007/978-981-13-1402-5_2

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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.
In the sub-field of quantum algorithms, physicists and computer scientist take classical computing algorithms and principles and see if there is a more efficient or faster approach implementable on a quantum computer, i.e. a ”quantum advantage”. We take random walks, a widely applicable group of classical algorithms, and move them into the quantum computing paradigm. Additionally, an introduction to a popular quantum search algorithm called Grover’s search is included to guide the reader to the development of a quantum search algorithm using quantum random walks. To close the gap between algorithm and hardware, we will look at using neutral-atom (also known as cold-atom) quantum computing to physically implement two types of quantum random walks and Grover’s algorithm.
Quantum computing promises a leap in performance over classical computing. Its computational power was revealed after the introduction of some quantum algorithms such as Grover's search algorithm. Many classical algorithms especially that deal with Error Correcting Codes are introduced to solve an exhaustive search problem. The quantum techniques promise an optimal search speed that is of special importance when the size of the searched domain is quite large. In this paper we devise the use of quantum search algorithm introduced by Grover to implement the viterbi algorithm (VA). Due to lack of resources and the nature of implementing quantum algorithms, only theoretical results are obtained. The use of quantum search algorithm showed that we can reduce the number of search computations exponentially. For example if the classical VA requires 262144 searching operations for a signalling length of 1024 intervals, the quantum algorithm will need only 512 searching operations when single search quantum viterbi algorithm (SSQVA) is used. And for the multi search quantum viterbi algorithm (MSQVA) it needs 16384 searching operations for the same signalling length.