  There are two general requirements to harness the computational power of
quantum mechanics: the ability to manipulate the evolution of an isolated
system and the ability to faithfully extract information from it. Quantum error
correction and simulation often make a more exacting demand: the ability to
perform non-destructive measurements of specific correlations within that
system. We realize such measurements by employing a protocol adapted from [S.
Nigg and S. M. Girvin, Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time
selection of arbitrary register-wide Pauli operators. Our implementation
consists of a simple circuit quantum electrodynamics (cQED) module of four
highly-coherent 3D transmon qubits, collectively coupled to a high-Q
superconducting microwave cavity. As a demonstration, we enact all seven
nontrivial subset-parity measurements on our three-qubit register. For each we
fully characterize the realized measurement by analyzing the detector
(observable operators) via quantum detector tomography and by analyzing the
quantum back-action via conditioned process tomography. No single quantity
completely encapsulates the performance of a measurement, and standard figures
of merit have not yet emerged. Accordingly, we consider several new fidelity
measures for both the detector and the complete measurement process. We measure
all of these quantities and report high fidelities, indicating that we are
measuring the desired quantities precisely and that the measurements are highly
non-demolition. We further show that both results are improved significantly by
an additional error-heralding measurement. The analyses presented here form a
useful basis for the future characterization and validation of quantum
measurements, anticipating the demands of emerging quantum technologies.
