Quantum logic for state preparation, readout, and leakage detection with binary subspace measurements

We discuss a quantum logic spectroscopy technique that uses the geometric phase gate interaction to implement quantum nondemolition (QND) measurements, distinguishing between two subspaces within a hyperfine manifold of a trapped ion. We then discuss how to use these binary subspace measurements for efficient, high-fidelity state preparation and measurement (SPAM) as well as nondestructive leakage detection. We show how to use (classical) error-correction methods to suppress SPAM error, at least to the extent the binary subspace measurements maintain QND purity. Suppressing SPAM error through redundant operations, rather than precise field engineering, could reduce some of the engineering complexity associated with building larger trapped-ion quantum computers.