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It is well established that the collective motion of ion crystals can be usedas a quantum bus for multi-qubit entanglement. However, as the number of ionsincreases, it becomes difficult to directly entangle ions far apart and resolveall motional modes of the ion crystal. We introduce a scalable and flexiblescheme for efficient entanglement between any pair of ions within a large ionchain, using an evenly distributed 50-ion crystal as an example. By performingamplitude and frequency modulation, we find high-fidelity pulse sequences thatprimarily drive a transverse motional mode with a wavelength of 4 ion spacings.We present two $500 \mu s$ pulses that can in theory suppress gate errors dueto residual motion to below $10^{-4}$, and observe a trade-off between gatepower and robustness against unwanted frequency offsets.

Entangling an arbitrary pair of qubits in a long ion crystal