Visible to the public Simulation of Modular Exponentiation Circuit for Shor's Algorithm in Qiskit

TitleSimulation of Modular Exponentiation Circuit for Shor's Algorithm in Qiskit
Publication TypeConference Paper
Year of Publication2020
AuthorsLarasati, H. T., Kim, H.
Conference Name2020 14th International Conference on Telecommunication Systems, Services, and Applications (TSSA
Keywords4-bit VBE quantum modular exponentiation circuit, adders, aforementioned circuit, Computational modeling, Ekert proposal, example simulation, exponentiation, integer factorization problem, Integrated circuit modeling, large-qubit quantum computer, Logic gates, pubcrawl, public key cryptography, Qiskit, Qiskit simulator, Quantum circuit, quantum computing, quantum gates, quantum modular exponentiation circuit, Qubit, Registers, Resiliency, RSA cryptosystems, Scalability, Shor's Algorithm incorporating, step-by-step manner, x mod 15 circuit
AbstractThis paper discusses and demonstrates the construction of a quantum modular exponentiation circuit in the Qiskit simulator for use in Shor's Algorithm for integer factorization problem (IFP), which is deemed to be able to crack RSA cryptosystems when a large-qubit quantum computer exists. We base our implementation on Vedral, Barenco, and Ekert (VBE) proposal of quantum modular exponentiation, one of the firsts to explicitly provide the aforementioned circuit. Furthermore, we present an example simulation of how to construct a 7xmod 15 circuit in a step-by-step manner, giving clear and detailed information and consideration that currently not provided in the existing literature, and present the whole circuit for use in Shor's Algorithm. Our present simulation shows that the 4-bit VBE quantum modular exponentiation circuit can be constructed, simulated, and measured in Qiskit, while the Shor's Algorithm incorporating this VBE approach itself can be constructed but not yet simulated due to an overly large number of QASM instructions.
Citation Keylarasati_simulation_2020