In this talk, we explore the implications of attempts to efficiently tune-up and calibrate mesoscale quantum computers on the optimal physical layout of the underlying quantum hardware. We introduce a previously proposed classical adaptive learning algorithm, Noise Mapping for Quantum Architectures (NMQA), and present several technical innovations that enable classical filtering of discrete projective measurements, useful for adaptively learning system-dynamics, noise properties or hardware performance variations in classically correlated measurement data. Using insights from sequential Monte-Carlo approaches, convergence properties of NMQA are discussed. In the second part of the talk, we focus on the specific challenge of calibrating ("mapping") spatially inhomogeneous noise fields or calibration errors using spectator qubits dedicated to the problem of sensing. Drawing on optimal approximation theory to dictate sampling locations, we present optimal sensor-qubit arrangements at the Padua points to reconstruct dephasing fields in 2D via Lagrange approximation methods. The performance of these Padua-inspired techniques is compared to NMQA, using the same qubit arrangement on hardware. Our results show that Padua-inspired techniques display optimal error scaling behavior relative to NMQA in ideal cases, and we probe the limits of these benefits as a function of measurement noise and spatial errors in qubit locations. Extensions to incorporate spatio-temporal dynamics are discussed. *This work partially supported by the ARC Cen-tre of Excellence for Engineered Quantum SystemsCE170100009, the US Army Research Office underContract W911NF-12-R-0012, and a private grant fromH. & A. Harley.