Noise-robust holonomic gates realized by the adiabatic non-Abelian geometric phase play a key role in quantum information processing. However, previous holonomic gates were realized via real pulses applied to Hermitian quantum systems. Here we extend the general form of non-Abelian holonomy to the non-Hermitian degenerate quantum systems. In addition, we show that the non-Abelian geometric phases can be generated via adiabatic cyclic evolution of the four-level tripod quantum system driven by complex pulses. Notably, this phase is purely geometric, obtained via the single-loop multipulse approach, and is employed to realize a set of universal holonomic gates. Furthermore, we demonstrate that this geometric quantum gate is robust against systematic errors from small perturbations in pulse parameters.

Close

PrevNext

View figure in article

• Geometric & topological phases
• Open quantum systems & decoherence
• Quantum computation
• Quantum control