Systematic-Error-Tolerant Multiqubit Holonomic Entangling Gates

Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose realize high-fidelity $(N+1)$-qubit controlled using Rydberg atoms confined in optical arrays or superconducting circuits. identify the scheme, deduce effective multibody Hamiltonian, determine working condition of multiqubit gate. Uniquely, gate is immune systematic errors, i.e., laser parameter fluctuations motional dephasing, as $N$ control largely remain very stable qubit space during operation. show that ${C}_{N}$-not can reach same level fidelity at given time $N\ensuremath{\le}5$ under suitable choice parameters, tolerance against errors parameters be further enhanced through optimal pulse engineering. In case atoms, proposed protocol intrinsically different from typical schemes based on blockade antiblockade. Our study paves an alternative way build robust with trapped It contributes current efforts develop scalable computation fabricable devices.