  Two-dimensional (2D) ion crystals have become a promising way to scale up
qubit numbers for ion trap quantum information processing. However, to realize
universal quantum computing in this system, individually addressed
high-fidelity two-qubit entangling gates still remain challenging due to the
inevitable micromotion of ions in a 2D crystal as well as the technical
difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates
between any ion pairs in a 2D crystal of four ions. We use symmetrically placed
crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve
an addressing crosstalk error below 0.1%. We design and demonstrate a gate
sequence by alternatingly addressing two target ions, making it compatible with
any single-ion addressing techniques without crosstalk from multiple addressing
beams. We further examine the gate performance versus the micromotion amplitude
of the ions and show that its effect can be compensated by a recalibration of
the laser intensity without degrading the gate fidelity. Our work paves the way
for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion
crystal.
