  Gate set tomography (GST) is a self-consistent and highly accurate method for
the tomographic reconstruction of a quantum information processor's quantum
logic operations, including gates, state preparations, and measurements.
However, GST's experimental cost grows exponentially with qubit number. For
characterizing even just two qubits, a standard GST experiment may have tens of
thousands of circuits, making it prohibitively expensive for platforms. We show
that, because GST experiments are massively overcomplete, many circuits can be
discarded. This dramatically reduces GST's experimental cost while still
maintaining GST's Heisenberg-like scaling in accuracy. We show how to exploit
the structure of GST circuits to determine which ones are superfluous. We
confirm the efficacy of the resulting experiment designs both through numerical
simulations and via the Fisher information for said designs. We also explore
the impact of these techniques on the prospects of three-qubit GST.
