T-ResiSat-QIP: A T-Cost Efficient, Decoherence- Resilient, Cascadable Quantum Saturation Adder for Quantum Image Processing

Reversible logic has become a fundamental paradigm in modern computing, serving as the theoretical basis for quantum computation. Clifford + T gates are used because of their robustness against decoherence faults in quantum circuits. However, the use of T gates introduces implementation challenges due to their relatively high cost. In quantum image processing, saturated arithmetic is essential to ensure that results, such as the sum of two numbers, remain within a strict valid range to prevent overflow. While a few quantum saturating adders exist, this work presents the first fault-tolerant Clifford + T-based saturating generator block. Its key innovation is a constant T-depth and low quantum cost, making it both cascadable and scalable for larger adders. Simulations in the Quirk tool confirm its accuracy, and results demonstrate a 26% T-depth and 13.3% T-count improvements of the proposed addition over current methods. This design applies to NEQR-based quantum image brightness adjustment.