Implementation of the quantum full-adder algorithm using integrated optics

One of the main challenges in quantum computing is implementing algorithms within quantum optical free-space and integrated circuits. This research focuses on the quantum addition algorithm, derived from the Deutsch-Jozsa algorithm, to advance quantum computing using optical technologies. The developed quantum optical integrated circuit is built on a hybrid substrate with interconnected components on a silicon dioxide base. Qubits and their states are arranged according to the requirements of each quantum algorithm. In the Fourier transform section, qubits act as propagation modes within silicon waveguides, with emitted photons representing the Fourier transform after traveling a distance of π/2. The phase-shifting section consists of two parts: one shifts the phase of incoming photons by π, while the other modulates this shift based on the quantum full adder algorithm. The first employs a photonic crystal for short phase shifts, which are adjusted via impurities in the silicon substrate and controlled by an electro-optic circuit. Additionally, single-mode waveguides made of silicon dioxide and air serve as qubits. By coupling photon amplitudes, a comparator circuit is triggered based on the generated output. Through these integrations, the sum of two quantum numbers can be represented at the output. This underscores the importance of designing and simulating a full adder within quantum optical integrated circuits to address the complexities inherent in quantum computing.