Systematic error tolerant multiqubit holonomic entangling gates.

Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach to implementing fault-tolerant quantum computation. We propose to realize high fidelity holonomic multiqubit controlled (C$_N$-NOT with $N$ control qubits) gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multi-body Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the $N$ control atoms largely remain in the much stable qubit space during the operation. We show that the gate time is independent of the number of the control qubits for moderate $N\le5$, and its tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves a new route to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superdonducting devices.