Half-Adder and Full-Adder Implementation with Continuous Variable Quantum Gates in a Photonic Quantum Computer

In this article, we report, to the best of our knowledge, for the first time, the design and simulation of half-adder and full-adder circuits implemented using continuous variable (CV) quantum gates within the framework of quantum photonics. Our approach supports the high-dimensional nature of CV and offers an alternative to the commonly used discrete variable (DV) systems for scalable and noise-resilient quantum computing architectures. We utilize Gaussian operations, displacement gates, and beamsplitter-based interferometric circuits to perform quantum arithmetic operations, utilizing CV systems' entanglement and superposition principles. Carefully engineered gate sequences and phase-space manipulations allow us to realize logic operations corresponding to classical addition, with each optical mode representing a computational basis state. We present two distinct circuit designs, one for a half adder and one for a full adder, each verified using a CV simulation environment. Our results highlight the potential of continuous platforms to implement arithmetic logic for hybrid classical-quantum processors. This work opens a new pathway towards optical quantum computing with compact, noise-tolerant logic modules using CV quantum information processing.