The tetrahedron equation was proposed by Zamolodchikov in 1980, and the 3D reflection equation was proposed by Isaev and Kulish in 1997, to describe the integrability of 3D lattice models. In this talk I introduce solutions to these equations by using quantum cluster mutations, based on joint works with Atsuo Kuniba, Xiaoyue Sun, Yuji Terashima and Junya Yagi. We develop the method introduced by Sun and Yagi in 2022, where they attached three types of quivers to wiring diagrams, and for each of them the quantum mutations yield the solution of the tetrahedron equation in terms of quantum dilogarithm functions. Our strategy is to embed the noncommuting algebra generated by quantum y-variables in the q-Weyl algebra associated with wiring diagrams. This approach enables a unified understanding of various solutions to the tetrahedron equation that were previously known separately, via quantum cluster algebras.