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TELKOMNIKA (Telecommunication Computing Electronics and Control)

Web-app realization of Shor’s quantum factoring algorithm and Grover’s quantum search algorithm

Arya Wicaksana, Anthony Anthony, Adjie Wahyu Wicaksono

Published Jun 1, 2020• 4 citations
Publisher

Abstract

Quantum algorithms are well-known for their quadratic if not exponential speedup over their classical counterparts. The two widely-known quantum algorithms are Shor’s quantum factoring algorithm and Grover’s quantum search algorithm. Shor’s quantum factoring algorithm could perform integer factorization in O(logN). Grover’s quantum search algorithm could solve the unsorted search problem in O(√N). However, both algorithms are introduced as theoretical concepts in the original papers due to the limitations of quantum technology at that time. In this paper, an improved way is presented to realize the two algorithms into a web application using state-of-the-art quantum technology. The web-app is designed and built considering the uses of a quantum simulator and libraries provided by ProjectQ and Rigetti Forest. The result shows that both algorithms are realizable into web-applications.

DOI
10.12928/telkomnika.v18i3.14755

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Quantum algorithms are well-known for their quadratic if not exponential speedup over their classical counterparts. The two widely-known quantum algorithms are Shor’s quantum factoring algorithm and Grover’s quantum search algorithm. Shor’s quantum factoring algorithm could perform integer factorization in O(logN). Grover’s quantum search algorithm could solve the unsorted search problem in O(√N). However, both algorithms are introduced as theoretical concepts in the original papers due to the limitations of quantum technology at that time. In this paper, an improved way is presented to realize the two algorithms into a web application using state-of-the-art quantum technology. The web-app is designed and built considering the uses of a quantum simulator and libraries provided by ProjectQ and Rigetti Forest. The result shows that both algorithms are realizable into web-applications.
The power of quantum mechanics, that is too complex for conventional computers, can be solved by an innovative model of computing known as quantum computing. Quantum algorithms can provide exponential speedups for some types of problems, such as many difficult mathematical ones. In this paper, we review some of the most important quantum algorithms for hard mathematical problems. When factoring large numbers, Shor's algorithm is orders of magnitude faster than any other known classical algorithm. The Grover's algorithm, which searches unsorted databases much more quickly than conventional algorithms, is then discussed.
Quantum computing introduces an efficient way for unfolding complex problems on computing systems. It uses concept of superposition and entanglement, & hence supports intrinsic parallelism for obtaining the speedup in context of time over classical computing. Quantum algorithms can be efficiently implemented over quantum computing system. Most popular quantum algorithms like Grover's and Shor's provide a great foundation to specifically design the algorithms. These algorithms work on improving the lower runtime bounds of classical algorithms. Grover's algorithm exhibits a quadratic polynomial speedup while searching an element among `N' elements unstructured database. The algorithmic strategy can be applied over various computer science related applications and some important are being considered in this article i.e. pattern matching, data mining and machine learning. This article explores quantum fundamentals; history based evolution followed by Grover's search algorithm in detail with cascading advantages, limitations & applications and also finally concludes with the significance of quantum computing & quantum algorithmic domains.
In 1994, Peter Shor discovered a polynomial time quantum algorithm for factoring and discrete logarithm. Two years later, in 1996, Lov Grover discovered a search algorithm which is quadratically better than conventional search. By now, each of the two algorithms has developed into a line of research which goes well beyond the original algorithm. Shor's algorithm has inspired the study of quantum Fourier sampling which has resulted in more quantum algorithms for number-theoretic and group-theoretic problems. Grover's algorithm has developed into the area of quantum query algorithms.I will survey the developments in quantum query algorithms. The topics will include: applications of Grover's algorithm to element distinctness and other problems, lower bounds on quantum algorithms and the use of quantum random walks to design better search algorithm. I will also describe how some of techniques in this area can be used as "quantum black boxes" in an otherwise classical algorithm.
Quantum computing has emerged as a revolutionary paradigm, holding immense potential to solve complex problems that classical computing struggles to address. This study explores the application of quantum computing in cryptography, with a specific focus on two major quantum algorithms: Shor’s algorithm for large number factorization and Grover’s algorithm for unstructured database searching. The main objective of this research is to compare the performance of these quantum algorithms with classical cryptographic methods in terms of computational efficiency and time. Shor’s algorithm, which can factorize large numbers in polynomial time, presents a significant threat to the security of public-key cryptosystems such as RSA, which rely on the difficulty of factoring large numbers. On the other hand, Grover’s algorithm offers a quadratic speedup for searching unstructured databases, making it highly relevant for symmetric key cryptography systems like AES. In this study, simulations of both algorithms were conducted using quantum simulators to assess their speed and effectiveness in solving cryptographic challenges. The results demonstrate that quantum algorithms significantly reduce the computation time compared to classical methods, with Shor’s algorithm efficiently solving factorization problems and Grover’s algorithm accelerating key searching processes. However, while these quantum algorithms show promise in improving cryptographic systems, the implementation of large-scale quantum computers remains a challenge. This research highlights the potential of quantum computing to revolutionize data security and underscores the need for further development in quantum algorithms and the transition to quantum-resistant cryptographic systems to safeguard against the threat posed by quantum computers.
Prime number factorization is a problem in computer science where the solution to that problem takes super-polynomial time classically. Shor’s quantum factoring algorithm is able to solve the problem in polynomial time by harnessing the power of quantum computing. The implementation of the quantum algorithm itself is not detailed by Shor in his paper. In this paper, an approach and experiment to implement Shor’s quantum factoring algorithm are proposed. The implementation is done using Python and a quantum computer simulator from ProjectQ. The testing and evaluation are completed in two computers with different hardware specifications. User time of the implementation is measured in comparison with other quantum computer simulators: ProjectQ and Quantum Computing Playground. This comparison was done to show the performance of Shor’s algorithm when simulated using different hardware. There is a 33% improvement in the execution time (user time) between the two computers with the accuracy of prime factorization in this implementation is inversely proportional to the number of qubits used. Further improvements upon the program that has been developed for this paper is its accuracy in terms of finding the factors of a number and the number of qubits used, as previously mentioned.
Quantum computing represents a paradigm shift in computational ability, offering exponentially faster processing for specific problems than traditional classical algorithms. This review provides a comprehensive assessment of the development and implications of algorithms specifically designed for quantum computing systems. Key quantum algorithms such as Shor’s algorithm for integer factorization and Grover’s algorithm for unstructured search have demonstrated potential quantum supremacy by outperforming their classical counterparts. We examine the theoretical underpinnings and practical challenges of implementing these algorithms, alongside exploring novel algorithmic frameworks emerging from quantum machine learning and error correction disciplines. Furthermore, the review discusses the profound implications of quantum algorithm development in cryptography, optimization, and simulation, which are poised to transform industries reliant on these computational tasks. Our analysis concludes with a perspective on future research directions and the barriers that must be overcome to realize the full potential of quantum algorithms in practical applications.