Scalable global gate on arbitrary ion-qubits

A quantum algorithm can be decomposed into a sequence consisting of single qubit and 2-
qubit entangling gates. To optimize the decomposition and achieve more efficient
construction of the quantum circuit, we can replace multiple 2-qubit gates with a single global
entangling gate. Here, we propose and implement a scalable scheme to realize the global
entangling gates on multiple 171Yb+ ion qubits by coupling to multiple motional modes
through external fields. Such global gates require simultaneously decoupling of multiple
motional modes and balancing of the coupling strengths for all the qubit-pairs at the gate time.
To satisfy the complicated requirements, we develop a trapped-ion system with fullyindependent control capability on each ion, and experimentally realize the global entangling
gates. As examples, we utilize them to prepare the Greenberger-Horne-Zeilinger (GHZ) states
in a single entangling operation, and successfully show the genuine multi-partite
entanglements up to four qubits with the state fidelities over 93.4%.