Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic
The Quantum Fourier Transform (QFT) grants competitive advantages, especially
in resource usage and circuit approximation, for performing arithmetic
operations on quantum computers, and offers a potential route towards a
numerical quantum-computational paradigm. In this paper, we utilize efficient
techniques to implement QFT-based integer addition and multiplications. These
operations are fundamental to various quantum applications including Shor's
algorithm, weighted sum optimization problems in data processing and machine
learning, and quantum algorithms requiring inner products. We carry out
performance evaluations of these implementations based on IBM's superconducting
qubit architecture using different compatible noise models. We isolate the
sensitivity of the component quantum circuits on both one-/two-qubit gate error
rates, and the number of the arithmetic operands' superposed integer states. We
analyze performance, and identify the most effective approximation depths for
quantum add and quantum multiply within the given context. We observe
significant dependency of the optimal approximation depth on the degree of
machine noise and the number of superposed states in certain performance
regimes. Finally, we elaborate on the algorithmic challenges - relevant to
signed, unsigned, modular and non-modular versions - that could also be applied
to current implementations of QFT-based subtraction, division, exponentiation,
and their potential tensor extensions. We analyze performance trends in our
results and speculate on possible future development within this computational
paradigm.
Robert A. M. Basili Wenyang Qian Shuo Tang Austin M. Castellino Mary Eshaghian-Wilner James P. Vary Glenn Luecke Ashfaq Khokhar