Extending Shor's quantum error correction circuits using quantum adders

Abstract

One of the critical limitations quantum computers are yet to overcome is quantum errors. Efforts have been made in quantum error correction fields to overcome them. However, since we are bound by the technology of this noisy intermediate-scale quantum era, it is important that we focus on the efficiency and optimization of our error correction circuits. In this paper, we present a way of extending quantum error correction circuits using quantum adders by utilizing the notion of majority voting over all the qubits. We use adder circuits and a comparator to achieve majority voting. We demonstrate how our proposed methodology exhibits a linear trend in the required number of quantum gates. Further, we confirm the accuracy and efficacy of our proposed methodology for optimizing the number of quantum gates through extensive simulation in IBM's Qiskit and compare them with existing literature.