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Ion trap systems are a leading platform for large scale quantum computers.Trapped ion qubit crystals are fully-connected and reconfigurable, owing totheir long range Coulomb interaction that can be modulated with externaloptical forces. However, the spectral crowding of collective motional modescould pose a challenge to the control of such interactions for large numbers ofqubits. Here, we show that high-fidelity quantum gate operations are stillpossible with very large trapped ion crystals, simplifying the scaling of iontrap quantum computers. To this end, we present analytical work that determineshow parallel entangling gates produce a crosstalk error that falls off as theinverse cube of the distance between the pairs. We also show experimental workdemonstrating entangling gates on a fully-connected chain of seventeen$^{171}{\rm{Yb}}^{+}$ ions with fidelities as high as $97(1)\%$.

Two-qubit entangling gates within arbitrarily long chains of trapped ions