  Quantum computational approaches to some classic target identification and
localization algorithms, especially for radar images, are investigated, and are
found to raise a number of quantum statistics and quantum measurement issues
with much broader applicability. Such algorithms are computationally intensive,
involving coherent processing of large sensor data sets in order to extract a
small number of low profile targets from a cluttered background. Target
enhancement is accomplished through accurate statistical characterization of
the environment, followed by optimal identification of statistical outliers.
The key result of the work is that the environmental covariance matrix
estimation and manipulation at the heart of the statistical analysis actually
enables a highly efficient quantum implementation. The algorithm is inspired by
recent approaches to quantum machine learning, but requires significant
extensions, including previously overlooked `quantum analog--digital'
conversion steps (which are found to substantially increase the required number
of qubits), `quantum statistical' generalization of the classic phase
estimation and Grover search algorithms, and careful consideration of projected
measurement operations. Application regimes where quantum efficiencies could
enable significant overall algorithm speedup are identified. Key possible
bottlenecks, such as data loading and conversion, are identified as well.
