Efficient quantum arithmetic operation circuits for quantum image processing

Efficient quantum circuits for arithmetic operations are vital for quantum algorithms. A fault-tolerant circuit is required for a robust quantum computing in the presence of noise. Quantum circuits based on Clifford+T gates are easily rendered fault-tolerant. Therefore, reducing the T-depth and T-Count without increasing the qubit number represents vital optimization goals for quantum circuits. In this study, we propose the fault-tolerant implementations for TR and Peres gates with optimized T-depth and T-Count. Next, we design fault-tolerant circuits for quantum arithmetic operations using the TR and Peres gates. Then, we implement cyclic and complete translations of quantum images using quantum arithmetic operations, and the scalar matrix multiplication. Comparative analysis and simulation results reveal that the proposed arithmetic and image operations are efficient. For instance, cyclic translations of a quantum image produce 50% T-depth reduction relative to the previous best-known cyclic translation.