  State preparation and measurement (SPAM) errors limit the performance of many
gate-based quantum computing architecures, but are partly correctable after a
calibration step that requires, for an exact implementation on a register of
$n$ qubits, $2^n$ additional characterization experiments, as well as classical
post-processing. Here we introduce an approximate but efficient method for SPAM
error characterization requiring the {\it classical} processing of $2^n \!
\times 2^n$ real matrices, but only $O(n^2)$ measurements. The technique
assumes that multi-qubit measurement errors are dominated by pair correlations,
which are estimated with $n(n-1)k/2$ two-qubit experiments, where $k$ is a
parameter related to the accuracy. We demonstrate the technique on the IBM and
Rigetti online superconducting quantum computers, allowing comparison of their
SPAM errors in both magnitude and degree of correlation. We also study the
correlations as a function of the register's geometric layout. We find that the
pair-correlation model is fairly accurate on linear arrays of superconducting
qubits. However qubits arranged in more closely spaced two-dimensional
geometries exhibit significant higher-order (such as 3-qubit) SPAM error
correlations.
