Comment on “Quantum multiplication algorithm based on the convolution theorem”

In their recent paper, Ramezani [] presented a quantum multiplication algorithm with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>O</a:mi><a:mrow><a:mo>(</a:mo></a:mrow><a:msqrt><a:mi>N</a:mi></a:msqrt><a:msup><a:mo form="prefix">log</a:mo><a:mn>2</a:mn></a:msup><a:mrow><a:mo>(</a:mo><a:mi>N</a:mi><a:mo>)</a:mo></a:mrow><a:mrow><a:mo>)</a:mo></a:mrow></a:mrow></a:math> operations, while the best classical algorithm [Harvey and van der Hoeven, ] needs <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>O</c:mi><c:mrow><c:mo>(</c:mo></c:mrow><c:mi>N</c:mi><c:mo form="prefix">log</c:mo><c:mo>(</c:mo><c:mi>N</c:mi><c:mo>)</c:mo><c:mrow><c:mo>)</c:mo></c:mrow></c:mrow></c:math> operations. This Comment corrects the incompleteness of the quantum complexity, showing that the classical method performs better. Published by the American Physical Society 2024