An Analysis of Quantum Factorization Algorithm by Simulation

T. Thamaraimanalan, Anandakumar Haldorai, Arulmurugan Ramu +1 more

Shor’s algorithm stands as a breakthrough in quantum computing due to its potential to factor large integers exponentially quicker than classical algorithms. However, implementing and evaluating this algorithm on real quantum computer hardware remains exciting due to qubit limitations, gate noise, and hardware constraints. This research presents a comprehensive performance evaluation of Shor’s algorithm using simulated quantum backends provided by Qiskit. A flexible and generic implementation is proposed, allowing dynamic input of integers to be factored, with randomized co-prime selection and automated circuit generation. The algorithm is tested on various semiprime numbers, such as 15, 21, and 35, using IBM’s Aer simulator. A major contribution of this work is the circuit-level analysis conducted both before and after transpilation. Metrics such as gate counts, circuit depth, and simulator runtime are extracted to assess scalability and resource requirements. High-resolution plots of the pre-transpiled circuits are saved to visualize algorithmic complexity, while post-transpilation metrics inform future quantum hardware feasibility. The output measurement distributions are analyzed to estimate periodicity and derive correct factors. The proposed implementation is compared with existing fixed-instance Shor demonstrations to highlight its flexibility and extensibility. Experimental results show consistent success in factor retrieval and provide valuable insight into circuit growth and complexity under realistic constraints. This analysis lays the groundwork for future adaptation to NISQ hardware and contributes to understanding Shor’s algorithm from both computational and architectural perspectives.

Takahiro Yamada, J. Niwa, Fumitaka Yura +1 more

Samuel Čarnoký

Meng Zhang, Jian Kang, Qian Wu +1 more

The Variational Quantum Eigensolver (VQE), as one of the most promising quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era, exhibits unique advantages in quantum chemistry simulations. It provides a novel approach to solving molecular electronic structure problems that are difficult to handle with classical computing. However, the performance of the VQE algorithm in quantum chemistry simulation is jointly affected by multiple factors, and its application in practical scenarios still faces numerous challenges. This paper first outlines the basic principles of the VQE algorithm and its core application scenarios in quantum chemistry simulation. Subsequently, it systematically analyzes the mechanism of the influencing factors, such as molecular system characteristics and algorithm parameter design, focusing on exploring how each factor specifically influences the results. Finally, the current research status and limitations in the optimization of influencing factors are summarized, and future research directions are proposed. This work aims to provide theoretical reference and technical support for improving the performance of quantum chemistry simulation based on the VQE algorithm and promoting its practical application.

I. Savran, M. Demirci, A.H. Yılmaz

Shor’s quantum algorithm is very important for cryptography, because it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor’s quantum algorithm on graphic processor units (GPU) and compare our results with Liquid, which is a Microsoft quantum simulation platform, and two classical CPU implementations. We evaluate 10 benchmarks for comparing our GPU implementation with Liquid and single-core implementation. The analysis shows that GPU vector operations are more suitable for Shor’s quantum algorithm. Our GPU kernel function is compute-bound, due to all threads in a block reaching the same element of the state vector. Our implementation has 52.5× speedup over single-core algorithm and 20.5× speedup over Liquid.

Xinhua Peng