Engineering Minimal-Complexity Clifford Circuits Controlled by Microwaves via Coherent Phonon-Mediated SiV$^{-}$ Centers in Diamond

Abstract

Engineering quantum circuits that use minimal resource requirements are essential for suppressing noise-induced errors and enhancing the performance of quantum processors. Here, we propose minimal-complexity hardware constructions of Clifford circuits for implementing new two-qubit Clifford gates, effectively expanding the available Clifford circuit library. The circuits are realized through engineered coherent phonon-mediated interactions between two subsets of negatively charged silicon-vacancy centers, each of which is independently controlled by microwave driving fields that modulate the effective Hamiltonian. In addition, we demonstrate that under appropriate microwave driving parameters, this setup can significantly reduce circuit depth, enabling more efficient gate execution and improved complexity speedup. Moreover, we investigate the impact of pulse-area errors in the proposed circuits to evaluate their robustness against systematic errors. The protocol shows potential compatibility with scalable quantum hardware for implementing advanced algorithms in future quantum technologies.