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A major current challenge in solid-state quantum computing is to scale qubit
arrays to a larger number of qubits. This is hampered by the complexity of the
control wiring for the large number of independently tunable interqubit
couplings within these arrays. One approach to simplifying the problem is to
use a qubit array with fixed Ising ($ZZ$) interactions. When simultaneously
driving a specific subset of qubits in such a system, the dynamics are confined
to a set of commuting $\mathfrak{su}$(2) subalgebras. Within these
$\mathfrak{su}$(2)s we describe how to perform $X$-gates and $\frac{\pi}{2}$
$ZZ$ rotations robustly against either leakage, which is the main source of
error in transmon qubits, or coupling fluctuations, which is the main source of
infidelity in flux or semiconductor spin qubits. These gates together with
virtual-$z$ gates form a universal set of gates for quantum computing. We
construct this set of robust gates for two-edge, three-edge, and four-edge
vertices, which compose all existing superconducting qubit and semiconductor
spin qubit arrays.
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