Title: Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform,
Abstract: We present some basic integer arithmetic quantum circuits, such as adders and
multipliers-accumulators of various forms, as well as diagonal operators, which
operate on multilevel qudits. The integers to be processed are represented in
an alternative basis after they have been Fourier transformed. Several
arithmetic circuits operating on Fourier transformed integers have appeared in
the literature for two level qubits. Here we extend these techniques on
multilevel qudits, as they may offer some advantages relative to qubits
implementations. The arithmetic circuits presented can be used as basic
building blocks for higher level algorithms such as quantum phase estimation,
quantum simulation, quantum optimization etc., but they can also be used in the
implementation of a quantum fractional Fourier transform as it is shown in a
companion work presented separately.