Quantum Modular Adder over GF(2n − 1) without Saving the Final Carry

Addition is the most basic operation of computing based on a bit system. There are various addition algorithms considering multiple number systems and hardware, studies for more efficient still ongoing. Quantum qubits as information unit asks design new because it is, physically, wholly different from existing frequency-based in which minimum bit. In this paper, we propose an quantum circuit modular addition, reduces gates depth. The proposed Galois Field GF(2n−1), important finite field basis domains, such cryptography. Its principle was ripple carry (RCA) algorithm, widely used computers. However, unlike conventional RCA, storage final not needed due to modifying diminished-1 modulo 2n−1 adders. Our adder can produce sum within range 0,2n−2 by fewer less For comparison, analyzed over GF(2n−1) previous performance qubits, gates, depth, simulated with IBM’s simulator ProjectQ.