  Parallel operations are important for both near-term quantum computers and
larger-scale fault-tolerant machines because they reduce execution time and
qubit idling. We propose and implement a pairwise-parallel gate scheme on a
trapped-ion quantum computer. The gates are driven simultaneously on different
sets of orthogonal motional modes of a trapped-ion chain. We demonstrate the
utility of this scheme by creating a GHZ state in one step using parallel gates
with one overlapping qubit. We also show its advantage for circuits by
implementing a digital quantum simulation of the dynamics of an interacting
spin system, the transverse-field Ising model. This method effectively extends
the available gate depth by up to two times with no overhead apart from
additional initial cooling when no overlapping qubit is involved. This is
because using a set of extra modes as additional quantum degrees of freedom is
nearly equivalent to halving the trap heating rate, doubling the laser and
qubit coherence time, and extending the controller memory depth by up to a
factor of two. This scheme can be easily applied to different trapped-ion
qubits and gate schemes, broadly enhancing the capabilities of trapped-ion
quantum computers.
