Quantum Array Multiplier

This paper proposes a new and improved implementation of a quantum integer multiplier. Performing arithmetic computations is sometimes a necessary step in the implementation of quantum algorithms. In this work, Quantum Fourier Transform is used in order to perform scalable arithmetic in a generic bit-width quantum system. In the phase domain, addition can be implemented through accumulated controlled rotations on the qubits’ state. Leveraging this, and inspired by the classical implementation of an array multiplier, a new integer multiplier is fully designed and tested in a quantum environment.The depth of a quantum circuit is the number of computational steps necessary to completion, and it is a key parameter that reflects on the performance of the design. The new design reduces the quantum depth of the design from the exponential order of the previously proposed designs to polynomial order.