Efficient Quantum Circuit for Karatsuba Multiplier

Abstract

The fundamental element of quantum computing is the quantum circuit. An efficient quantum circuit saves quantum hardware resources by reducing the number of gates without increasing the number of qubits. Quantum circuits with many qubits are very difficult to realize. Thus, the number of qubits is an important parameter in a quantum circuit design. Using reversible logic in quantum circuits has many advantages such as diminishing power consumption, reducing heat propagation and decreasing quantum cost, ancilla inputs, and garbage outputs that lead to increased performance of quantum computers. Quantum circuits for arithmetic operations such as addition, subtraction, and multiplication are required in the implementation of quantum circuits for many quantum algorithms in this area. In this article two novel designs for GF(2n) multiplier using Karatsuba algorithm have been proposed that have been proved to have an improvement in qubits, garbage outputs, and ancilla inputs when it comes to comparison with recent research that have been done concerning this field. Bennett’s garbage removal strategy with the SWAP gate is used to remove garbage output from existing works in order to establish a fair comparison to existing work.