Dephasing-Protected Scalable Holonomic Quantum Computation on a Rabi Lattice

Holonomic quantum computing has attracted much attention in achieving robust and high-fidelity quantum gates owing to its built-in noise-resilience features. Here in this work, we propose an experimentally feasible scheme to realize scalable nonadiabatic non-Abelian holonomic gates in Rabi lattices, where each building block favors ultrastrong coupling and accordingly is portrayed by a quantum Rabi model (QRM). The polariton states with the lowest two energies in the QRM effectively simulate a spin-half system and thus constitute a logical qubit. In contrast to the existing schemes of using ancillary levels, our holonomic operations are performed with the aid of neighboring QRMs acting as ancillary qubits. Employing the two-tone driving scheme onto the physical system, various noncommutable single-qubit and nontrivial two-qubit holonomic gates are applicable on the computational basis, in which all-resonant control is employed and this guarantees fast speed and consequently high fidelities. In addition, our scheme exhibits a unique advantage of being immune to dephasing noises as a result of intrinsic characteristics of the ultrastrong coupling and the QRM. Therefore, this scheme prompts the integration of ultrastrong coupling and geometric properties to mitigate the negative effect of errors and decoherence. Ultimately, holonomic quantum gates incorporated in QRMs with all-resonant control may enable reaching the accuracy threshold for scalable fault-tolerant quantum-information processing within and beyond the ultrastrong couping regime.