  We propose a new scalable platform for quantum computing (QC) -- an array of
optically trapped symmetric-top molecules (STMs) of the alkaline earth
monomethoxide (MOCH$_3$) family. Individual STMs form qubits, and the system is
readily scalable to 100 to 1000 qubits.STM qubits have desirable features for
quantum computing compared to atoms and diatomic molecules. The additional
rotational degree of freedom about the symmetric top axis gives rise to
closely-spaced opposite parity $K$-doublets that allow full alignment at low
electric fields, and the hyperfine structure naturally provides magnetically
insensitive states with switchable electric dipole moments. These features lead
to much reduced requirements for electric field control, provide minimal
sensitivity to environmental perturbations, and allow for 2-qubit interactions
that can be switched on at will. We examine in detail the internal structure of
STMs relevant to our proposed platform, taking into account the full effective
molecular Hamiltonian including hyperfine interactions, and identify useable
STM qubit states. We then examine the effects of the electric dipolar
interaction in STMs, which not only guide the designing of high-fidelity gates,
but also elucidate the nature of dipolar spin-exchange in STMs. Under realistic
experimental parameters, we estimate that the proposed QC platform could yield
gate errors at the $10^{-3}$ level, approaching that required for
fault-tolerant quantum computing.
