A Reproducible Educational Demonstration of Grover's Quantum Search Algorithm Using Qiskit

Yuan Sun, Martin Lichtman, K.R. Baker +1 more

Lasha Janelidze, Mariam Janelidze

The work presents a demonstration of functional understanding and practical implementation of quantum computing processes. The project considers both quantum operations (for example, superposition of qubits using Hadamard gates) and complex algorithms, such as Grover's quantum search algorithm. This algorithm is used to optimize the search for a specifically labeled element in an n-qubit space and is one of the main demonstrations of the quantum speedup that gives quantum computing an advantage over classical models. The presented codes are divided into independent, modular functions, which reflects the observance of functional programming principles in quantum algorithms. It is these systematic calculations that improve the transparency, accessibility, and reusability of the code, which is critically important in a quantum development environment where experimentation and multiple testing of algorithms are widely used. The code was simulated using Qiskit's "Aer", which provides multishot execution and statistical analysis of the results. In addition, the implementation of Grover's algorithm used oracle modeling.

Manuel Benavent-Lledó, David Ortiz-Pérez, David Mulero-Pérez +2 more

Ahcène Bounceur, Mohammad Ali A. Hammoudeh, Bamidele Adebisi +1 more

This chapter examines Grover's algorithm, a quantum algorithm known for its efficacy in searching unsorted databases. Starting with a theoretical exposition complemented by geometric explanations and exemplified through iterative demonstrations, readers gain a clear understanding of the algorithmic principles at play. Then, this chapter examines the quantum domain, the exposition encompasses a comprehensive breakdown of the quantum circuit's construction, describing the specific roles of each constituent in facilitating algorithmic execution. Grover's algorithm is known for its remarkable ability to significantly reduce the computational resources required for executing the brute-force search problem. The chapter concludes with practical showcases utilising the Qiskit programming framework, thereby demonstrating the algorithm's scalability and practical utility across varying problem dimensions.

Yulun Wang, Robert J. Harrison, Predrag Krstić

Varun Barthwal, Aditya Raj Thakur, Pradeep Rana

Grover's algorithm, which was discovered in 1996, is faster than any classical algorithm can ever be. Quantum systems are in a superposition of states and can examine multiple data simultaneously. This work conducted a comprehensive analysis to understand how Grover's algorithm works. Grover's search provides quadratic speed in comparison to the classical one; it explores target data in the unstructured database. Grover search starts with the superposition of all Qubits, which results in the same amplitude for all data points. To achieve superposition, the Hadamard gate was applied to all Qubits. Further, a black box function named Oracle is applied to mark the desired state. In the next phase, amplitude amplification is done, which enhances the probability of the desired data point. Thus, Grover's search yields results with an O (√ N) complexity, while its counterpart classical algorithm searches the desired data point with an O (N) complexity. Experiments have been performed on the Qiskit simulator using 2 and 3 qubits for the detailed analysis of Grover's search.