Analysis and Implementation of Caroline Fedele1, Asai Asaithambi2 1Department of Physics, University of North Florida, 2School of Computing, University of North Florida

Objectives Relevance to Cybersecurity Plan to Utilize Quantum Regime Conclusion

• Develop new circuit models & reliable method It is vital we study quantum computing and be pre- Necessary steps: background research There is currently a gap between proposed supe-

for quantum processing pared when physical systems become sufficiently ad- 1 Mathematical & literature review rior quantum solutions and problems demonstrably • Analyze execution time complexity and vanced, particularly because of its threat to encryp- • • understand fundamental physics - quantum mechanics, solved using quantum algorithms. By following the memory required for the solution of some tion integrity. Almost all methods governing secure especially superposition and entanglement steps proposed in this research plan, coming one step data transmission are based on one difficult math • understand mathematics of parallel computing and closer to closing that gap between theory and prac- classical problems using both systems development • Simulate Shor’s algorithm for quantum integer problem that makes up the RSA cryptosystem: the • scour existing literature, know what has been tried tice. It is important to explore and advance our knowledge of quantum computing so we are pre- factorization, showing break down of classical problem of finding two prime factors of large inte- 2 Investigation of classical vs. quantum algorithms 100 • RSA cryptography scheme. gers (order of 10 digits). One quantum algorithm, • program classical algorithm using java, obtain time pared for when it, and so that in the future our Shor’s algorithm, breaks this down completely. complexity & memory information understanding of encryption is deepened and new This algorithm utilizes as well as • analyze problems mathematically to develop/understand quantum-proof methods can be developed. quantum algorithms What is Quantum Computing? existing quantum algorithms, the quantum Fourier 3 Implementation of Shor’s Algorithm • State of project: much of technical transform and modular , to reduce • • Use QISkit (IBM’s online quantum tool) for existing background review has been completed. Quantum computing is a new and very powerful this from an NP-problem (exponential time com- quantum algorithms to develop reliable approach. Investigation of quantum algorithms and paradigm in the field of computing, capable of revo- plexity) to a P-problem (polynomial time complex- • demonstrate approach and build quantum circuit for implementation of Shor’s algorithm are the Shor’s algorithm. lutionizing capabilities of many industries including ity). proposed next steps of this study. the medical field, materials science, economics, ma- chine learning, and cybersecurity. Quantum com- Key Goal: A Reliable & Accurate Quantum System puters are now being physically developed at IBM and Google but there exists a gap between what Building circuits of existing quantum algorithms, including Shor’s algorithm, they can do theoretically and what has been put and investigating possible new algorithms. into practice. The aim of this research is to help close that gap. We will build quantum circuits to represent algorithms and test in a quantum com- puter simulation. The inherent parallelism of quan- Physics & Mathematics Expected outcome tum computing allows us to efficiently solve prob- Superposition: allows qubit to be in state of 0 Figure 5:IBM 53-qubit Quantum Computer lems classical computers cannot. We observe quan- IO} --iH-1---- tum computing supremacy with problems deemed and 1 simultaneously. A bloch sphere (below) rep- intractable: the solution can only be found through resents qubit state space. Jo) - H References exhaustive search. Among these is one extremely IO ) z relevant to cybersecurity, known as Shor’s algo- Jo) - H . ··------1 l T.t [1] Martonosi, M. and Roetteler, M. “Next Steps 2 0 .u (121 ~ rithm, an efficient algorithm for integer factoriza- 8 11 } I U a - in Quantum Computing: Computer Science’s Role.” tion, which breaks down well-established methods -----. --... : ' Figure 3:example Shor’s algorithm subroutine November 2018. of cryptography. An aim of this research we will y [2] Baumhof, Andreas. “Breaking RSA Encryption specifically demonstrate how Shor’s algorithm can X Using qiskit, a quantum computer simulation, we – An Update on the State-of-the-Art.” June 2019. be built in a quantum system. can register qubits to the appropriate functions for a given algorithm, and thus build quantum algo- 11 ) Acknowledgements Figure 2:Bloch sphere: visualization of qubit state-space rithms. Many thanks to my mentor, Asai Asaithambi, for instructing Qubit: represented by any 2-D superposition of me in this subject, and to the UNF Physics and Computing states. • • departments for facilitating this opportunity. Fourier Transform: key transformation acting on a quantum state. Modular Exponentiation: method of exponen- tiation performed over a particular value, the mod- UNIVERSITY of· NORTH FLORIDA. Figure 1:qubit graphic rendering ulus, another key algorithm in quantum computing. Figure 4:Qiskit: program for building quantum circuits