Quantum-Fourier-transform-based quantum arithmetic with qudits

We present some basic integer arithmetic quantum circuits, such as adders and multiplier-accumulators of various forms, which operate on multilevel qudits. The integers to be processed are represented in an alternative basis after they have been Fourier transformed. Several circuits operating Fourier-transformed appeared the literature for two-level qubits. Here we extend these techniques qudits, may offer advantages relative qubit implementations. presented here can used building blocks higher level algorithms phase estimation, simulation, optimization, etc. Detailed decomposition is given down elementary single- two-qudit gates most appropriate physical implementation. A complexity analysis this step it shown that depth linear number qudits employed quadratic dimension each qudit while their cost dimension.