Robust Quantum Arithmetic Operations with Intermediate Qutrits in the NISQ-era

Numerous scientific developments in this NISQ-era (Noisy Intermediate Scale Quantum) have raised the importance for quantum algorithms relative to their conventional counterparts due to its asymptotic advantage. For resource estimates in several quantum algorithms, arithmetic operations are crucial. With resources reported as a number of Toffoli gates or T gates with/without ancilla, several efficient implementations of arithmetic operations, such as addition/subtraction, multiplication/division, square root, etc., have been accomplished in binary quantum systems. More recently, it has been shown that intermediate qutrits may be employed in the ancilla-free frontier zone, enabling us to function effectively there. In order to achieve efficient implementation of all the above-mentioned quantum arithmetic operations with regard to gate count and circuit-depth without T gate and ancilla, we have included an intermediate qutrit method in this paper. Future research aiming at reducing costs while taking into account arithmetic operations for computing tasks might be guided by our resource estimations using intermediate qutrits. Thus the enhancements are examined in relation to the fundamental arithmetic circuits. The intermediate qutrit approach necessitates access to higher energy levels, making the design susceptible to errors. We nevertheless find that our proposed technique produces much fewer errors than the state-of-the-art work, more specifically, there is an approximately 20% decrease in error probability for adder with 20 number of qubits. Similarly for multiplier and square root, the in error probability is nearly 20% for 5 number of qubits and 10 number of qubits respectively. We thus demonstrate that the percentage decrease in the probability of error is significant due to the fact that we achieve circuit efficiency by reducing circuit-depth in comparison to qubit-only works.