A Computation‐Enhanced High‐Dimensional Quantum Gate for Silicon‐Vacancy Spins

Abstract Qudit‐based quantum gates in high‐dimensional (HD) Hilbert space offer a viable route toward effectively accelerating the speed of quantum computing and performing complex quantum logic operations. In this study, an innovative 2‐qudit HD controlled‐SUM (CSUM) gate designed for four silicon‐vacancy spins is introduced, in which the first two electron‐spin states in silicon‐vacancy centers are encoded as the control qudit, and the other ones as the target qudit. The proposed protocol is implemented with assistance of an ancillary photon that serves as a common‐data bus linking four motionless silicon‐vacancy spins placed in four independent single‐sided optical nanocavities. Moreover, the CSUM gate works deterministically with the corresponding single‐qubit feed‐forward operation based on diverse outcomes of the single‐photon detectors to be directed against the ancillary photon. Further, it can be potentially generalized to other solid‐state quantum systems. Under current technological conditions, the 2‐qudit CSUM gate exhibits both high efficiency and fidelity.