Shor's Algorithm – ORACLE Design for Perfect Squares

Shor’s algorithm is a groundbreaking quantum computation method engineered to uncover the dual prime factors of an integer formed from these primes. Over the years, numerous research teams have embarked on the journey to harness this algorithm’s power. Yet, their efforts have successfully factorized numbers like 15, 21, 35, and others. This limitation arises from the challenges inherent in quantum hardware, which struggles to manage an abundance of qubits efficiently. The numbers 15, 21, and 35 share a common trait: they can be expressed as the product of two distinct prime factors. In contrast, this paper focuses on the design of an oracle to implement Shor’s algorithm for a unique category of integers - perfect squares. To illustrate, we chose the perfect square 49 as our target and shared our observations and findings regarding this specialized application of Shor’s algorithm.