International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-8, Issue-6S3, September 2019 52 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: F10090986S319/2019©BEIESP DOI: 10.35940/ijeat.F1009.0986S319 Abstract: 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. Index Terms: prime factorization, projectQ, quantum algorithm, Shor. I. INTRODUCTION Quantum mechanics is a fundamental theory in physics which describes the inner workings of the universe on the smallest energy scale [1]. This fundamental theory establishes new understandings and possibilities previously untapped by classical physics [2]. Today the quantum computer is one of the biggest scientific breakthroughs in the 20th century. A quantum computer is made by infusing the theory of quantum mechanics into computer science. It harnesses the power of quantum mechanics to perform computation [2], [3]. Thus, a quantum computer allows new kinds of computations which are previously impossible to be done in a classical computer [3]. IBM Q System One (IBM Q) is the first quantum computer that is publicly available through an online platform [4]. This quantum computer is able to simulate the bondings of elements, the learning process of artificial Revised Manuscript Received on September 22, 2019. Adjie Wahyu Wicaksono, Department of Informatics, Universitas Multimedia Nusantara, Tangerang - 15810, Indonesia. Arya Wicaksana, Department of Informatics, Universitas Multimedia Nusantara, Tangerang - 15810, Indonesia. intelligence, and optimize the process of quantum computation itself [4]. Major challenges in developing a quantum computer drive engineers to create a platform that enables the simulations of quantum computers [5]. ETH Zurich has a publicly accessible Python library and framework that simulates quantum computation on a classical computer named ProjectQ [6]. This library uses its own simulator and compiler developed by ETH Zurich to compile and execute quantum programs on a classical computer [6]. ProjectQ contains FermiLib, plugins for FermiLib, as well as compatibility with OpenFermion, all of which are open- source projects for quantum simulation algorithms. All examples that work with these frameworks naturally work with ProjectQ [5]. ProjectQ also provides a tutorial of Shor’s algorithm implementation using the framework. In comparison with another simulator such as QDK (Quantum Development Kit) which only provide an example in the documentation. Moreover, there is no implementation of Shor’s algorithm available yet in neither pyQuil nor Qiskit [5]. The availability of the implementation of Shor’s algorithm in ProjectQ encourages another implementation of Shor’s quantum factoring algorithm to be done using the framework. This is due to the fact that the framework already has sufficient support for implementing Shor’s quantum factoring algorithm. Quantum Computing Playground is another quantum computer simulator that was developed by a group of Google engineers in 2014 [7]. It uses QScript scripting language and compiler to simulate a quantum computer and available for public use. The scripting language is specifically built for the Quantum Computing Playground website [7]. The simulator is able to simulate quantum computations up to 22-qubits and offers its own implementation of Shor’s and Grover’s quantum algorithm for public use [7]. One of the usages of quantum computing is integer factorization [8]. This is a big discovery in mathematics and computation because this process takes super-polynomial time using a classical computer [9]. In number theory, this problem is called integer factorization problem. Integer factorization is the process of breaking down a composite integer into smaller ones that when multiplied back produces the initial value [10]. In fact, this problem is used as the fundamental security factor in the RSA cryptography system [11]. In 1994, Peter W. Shor discovers the quantum factoring algorithm that is able to solve the integer factorization Implementation of Shor’s Quantum Factoring Algorithm using ProjectQ Framework Adjie Wahyu Wicaksono, Arya Wicaksana