Patenting Quantum Computing Innovations – Part 5: Shor’s Algorithm and Conclusions

Shor’s algorithm efficiently factors large integers into their prime factors by reducing the problem to a period-finding task, which can be solved much more efficiently on a quantum computer than on a classical one. The algorithm involves preparing a quantum superposition of inputs and preparing a quantum gate to evaluate a modular exponentiation function. It then applies quantum phase estimation to extract the period of this function. This involves applying controlled powers of the quantum gate for modular exponentiation and then performing an inverse quantum Fourier transform to obtain information about the period. Once the period is determined, a classical algorithm…