Super-Robust Nonadiabatic Holonomic Quantum Computation in coherence-protected Superconducting Circuits

The schmeme of nonadiabatic holonomic quantum computation (NHQC) offers an error-resistant method for implementing quantum gates, capable of mitigating certain errors. However, the conventional NHQC schemes often entail longer operations concerning standard gate operations, making them more vulnerable to the effects of quantum decoherence. In this research, we propose an implementation of the Super-Robust NHQC scheme within the Decoherence-Free Subspace (DFS). SR-NHQC has demonstrated robustness against Global Control Errors (GCEs). By utilizing capacitance-coupled transmon qubits within a DFS, our approach enables universal gate operations on a scalable two-dimensional square lattice of superconducting qubits. Numerical simulations demonstrate the practicality of SR-NHQC in DFS, showcasing its superiority in mitigating GCEs and decoherence effects compared to conventional NHQC schemes. Our work presents a promising strategy for advancing the reliability of quantum computation in real-world applications.