Prepare Linear Distributions with Quantum Arithmetic Units.

Quantum arithmetic logic units (QALUs) perform essential arithmetic operations within a quantum framework, serving as the building blocks for more complex computations and algorithms in quantum computing. In this paper, we present an approach to prepare linear probability distributions with quantum full adders. There are three main steps. Firstly, Hadamard gates are applied to the two input terms, preparing them at quantum states corresponding to uniform distribution. Next, the two input terms are summed up by applying quantum full adder, and the output sum is treated as a signed integer under two's complement representation. By the end, additional phase -1 is introduced to the negative components. Additionally, we can discard either the positive or negative components with the assistance of the Repeat-Until-Success process. Our work demonstrates a viable approach to prepare linear probability distributions with quantum adders. The resulting state can serve as an intermediate step for subsequent quantum operations.