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The Quantum Fourier Transform (QFT) grants competitive advantages, especiallyin resource usage and circuit approximation, for performing arithmeticoperations on quantum computers, and offers a potential route towards anumerical quantum-computational paradigm. In this paper, we utilize efficienttechniques to implement QFT-based integer addition and multiplications. Theseoperations are fundamental to various quantum applications including Shor'salgorithm, weighted sum optimization problems in data processing and machinelearning, and quantum algorithms requiring inner products. We carry outperformance evaluations of these implementations based on IBM's superconductingqubit architecture using different compatible noise models. We isolate thesensitivity of the component quantum circuits on both one-/two-qubit gate errorrates, and the number of the arithmetic operands' superposed integer states. Weanalyze performance, and identify the most effective approximation depths forquantum add and quantum multiply within the given context. We observesignificant dependency of the optimal approximation depth on the degree ofmachine noise and the number of superposed states in certain performanceregimes. Finally, we elaborate on the algorithmic challenges - relevant tosigned, unsigned, modular and non-modular versions - that could also be appliedto current implementations of QFT-based subtraction, division, exponentiation,and their potential tensor extensions. We analyze performance trends in ourresults and speculate on possible future development within this computationalparadigm.

Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic