Hadamard gate realization based on quantum Fourier transform for the creation of quantum numbers in the integrated optical domain

One of the most significant challenges in quantum computing is the variability in implementing quantum algorithms across different chips. In this work, we present a Hadamard photonic gate based on the quantum Fourier transform, which superimposes several numbers encoded in the classical domain. We recognize that various mathematical operations - such as addition, subtraction, multiplication, division, and other complex calculations - are typically processed separately for each nth number in classical computers. This approach consumes considerable memory space and results in slower processing speeds as the number of bits increases. With the advancements provided in this work, we can eliminate the need for multiple memory spaces, allowing all numbers to be processed simultaneously in a single computation step. This is a key reason why quantum computers are significantly faster than their classical counterparts. Notably, as the number of bits increases, the number of processes remains consistent, enabling the same operations to be performed without requiring additional memory capacity. We have designed this algorithm using an optical integrated circuit that includes a silicon dioxide waveguide in an air bed, operating at a wavelength of 1.55 µm. Importantly, this circuit can not only be implemented independently on hybrid chips but also integrated into quantum monolithic chips based on Silicon Dioxide-Air optical waveguides as a key component of the overall structure.