Biblio

Quantum computing is an emerging field that depends upon the basic properties of quantum physics and principles of classical systems. This leads a way to develop systems to solve complex problems that a classical system cannot do. In this article, we present simple methods to implement logic circuits using quantum gates. Logic gates and circuits are defined with quantum gates using Qiskit in Python. Later, they are verified with quantum circuits created by using IBM Quantum. Moreover, we propose a way of instantiating the basic logic circuits to design high-end logic expressions. As per our knowledge, the proposed simple approach may be helpful to solve the complex logical problems in near future.

This 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.