Biblio

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.

Quantum technology is a new field of physics and engineering. In emerging areas like Quantum Cryptography, Quantum Computing etc, Quantum circuits play a key role. Quantum circuit is a model for Quantum computation, the computation process of Quantum gates are based on reversible logic. Encoder and Decoder are designed using Quantum gates, and synthesized in the QCAD simulator. Quantum error correction (QEC) is essential to protect quantum information from errors due to quantum noise and decoherence. It is also use to achieve fault-tolerant quantum computation that deals with noise on stored information, faulty quantum gates and faulty measurements.