The focus of this study is on developing a framework for a Quantum Algorithm Processing Unit (QAPU) with the hybrid architecture for classical-Quantum algorithms. The framework is used to increase the implementation performance of Quantum algorithms and design Quantum Processing Units (QPU). The framework shows a general plan for the architecture of Quantum processors who is capable of run the Quantum algorithms. In particular, the QAPU can be used as a Quantum node to design a Quantum multicomputer. At first, the hybrid architecture is designed for the Quantum algorithms. Then, the relationship between the classical and the Quantum part of hybrid algorithms is extracted, and main stages of the hybrid algorithm are developed. Next, the framework of the QAPU is designed.Furthermore, the framework is implemented and simulated for the existing Quantum algorithms on a classic computer.It is shown that the framework is appropriate for Quantum algorithms.