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New Optimized Grover's Algorithm Optimization of Grover's algorithm: with quantum simulating

Idhant Sood, Ahaan Sirohia, Arjun Dev Juneja

Published May 23, 2025• 0 citations
Publisher

Abstract

The paper below shows an optimized algorithm to perform Grover’s Algorithm on classical computers for high no. of states in reasonable times.
DOI
10.36227/techrxiv.174803113.34775460/v1

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Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum mechanics, the correctness of quantum algorithms is difficult to guarantee through traditional simulation methods. By contrast, the fundamental concepts and mathematical structure of Grover's algorithm can be formalized into logical expressions and verified by higher-order logical reasoning. In this paper, we formally model and verify Grover's algorithm in the HOL Light theorem prover. We focus on proving key properties such as the unitarity of its oracle and diffusion operators, the monotonicity of the success probability with respect to the number of iterations, and an exact expression for the optimal iteration count. By analyzing a concrete application to integer factorization, we demonstrate the practicality and prospects of our work.
This paper illustrated the optimality of Grover quantum search algorithm, and simulated the number of iterations and the specific implementation steps of quantum search algorithm with QCL in Linux operating systems, then validated the time complexity of Grover's quantum searching algorithm is O(√(N)) while the algorithm's time complexity on classical computers is O(N). The Grover quantum search algorithm were shown to improve the performance significantly in the random database search problem. This conclusion was drawn from the simulation in the Linux operating systems adopted to quantum computation language. The present study highlighted the importance of high efficiency of the Grover quantum search algorithm to achieve the best possible performance in such cases. The existence of such efficiency is an outstanding advantage of quantum search algorithm over the conventional approach.
In this work, we study the application of quantum computing to complex engineering simulations and decisions. Using these quantum algorithms like Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), Quantum Support Vector Machine (QSVM) and Grover’s Algorithm, we will optimize computational efficiency, accuracy and diversity of solutions in engineering. It was performed with a comparative analysis with classical algorithms based on performance metrics such as accuracy of solution, execution time, and optimality of the decision. Analysis of experimental results showed QAOA produces a 92.3% solution accuracy, higher than that (88.6%) of classical simulated annealing and (85.4%) genetic algorithms. Similarly, VQE achieved 27% reduction in execution time versus the classical equivalent and QSVM achieved 94.1% classification accuracy on engineering pattern recognition tasks. Grover’s Algorithm also resulted in a 3.7x faster search efficiency in decision oriented simulation. Finally, the study shows that quantum inspired models can perform efficiently on large scale and highly complex engineering problems. These findings provide a major leap in realizing the capability to harness quantum technologies for real time, scalable decision making in structural analysis, lifecycle management and intelligent system design. Such results make way for future developments of hybrid quantum classical computing frameworks that could be deployed in industry.