Quantum-Fourier-transform-based quantum arithmetic with qudits

摘要

We present some basic integer arithmetic quantum circuits, such as adders andmultipliers-accumulators of various forms, as well as diagonal operators, whichoperate on multilevel qudits. The integers to be processed are represented inan alternative basis after they have been Fourier transformed. Severalarithmetic circuits operating on Fourier transformed integers have appeared inthe literature for two level qubits. Here we extend these techniques onmultilevel qudits, as they may offer some advantages relative to qubitsimplementations. The arithmetic circuits presented can be used as basicbuilding blocks for higher level algorithms such as quantum phase estimation,quantum simulation, quantum optimization etc., but they can also be used in theimplementation of a quantum fractional Fourier transform as it is shown in acompanion work presented separately.