An optimized quantum circuit for converting from sign–magnitude to two’s complement

Abstract

Nowadays, one of the critical issues to implement quantum algorithms is the required number of elementary gates, qubits and delay. Current quantum computers and simulators are mainly prototypes, and there is a lack of computational resources. Therefore, it is necessary to optimize the quantum operations to reduce the necessary number of gates and qubits. This work presents a novel reversible circuit which is able to convert signed binary numbers to two’s complement of N digits in a quantum environment. The depth of the circuit is O(log N). It is based on the fastest out-of-place carry look-ahead addition quantum circuit currently available. This addition circuit has been adapted to make the conversion using the minimum number of gates and qubits, being faster than other adder circuits. A robust metric has been used to measure the quantum cost, delay, ancilla inputs and garbage outputs of the proposed converter. Moreover, it has been compared with others described in the literature.