Realizing Scalable Conditional Operations through Auxiliary Energy Levels

In the noisy intermediate-scale quantum (NISQ) era, flexible quantum operations are essential for advancing large-scale quantum computing, as they enable shorter circuits that mitigate decoherence and reduce gate errors. However, the complex control of quantum interactions poses significant experimental challenges that limit scalability. Here, we propose a transition composite gate scheme based on transition pathway engineering, which digitally implements conditional operations with reduced complexity by leveraging auxiliary energy levels. Experimentally, we demonstrate the controlled-unitary (CU) family and its applications. In entangled state preparation, our CU gate reduces the circuit depth for three-qubit Greenberger-Horne-Zeilinger (GHZ) and W states by approximately 40-44% compared to circuits using only CZ gates, leading to fidelity improvements of 1.5% and 4.2%, respectively. Furthermore, with a 72% reduction in circuit depth, we successfully implement a quantum comparator-a fundamental building block for quantum algorithms requiring conditional logic, which has remained experimentally challenging due to its inherent circuit complexity. These results demonstrate the scalability and practicality of our scheme, laying a solid foundation for the implementation of large-scale quantum algorithms in future quantum processors.