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Performing efficient quantum computer tuneup and calibration is essential forgrowth in system complexity. In this work we explore the link betweenfacilitating such capabilities and the underlying architecture of the physicalhardware. We focus on the specific challenge of measuring (``mapping'')spatially inhomogeneous quasi-static calibration errors using spectator qubitsdedicated to the task of sensing and calibration. We introduce a novelarchitectural concept for such spectator qubits: arranging them spatiallyaccording to prescriptions from optimal 2D approximation theory. We show thatthis insight allows for efficient reconstruction of inhomogeneities in qubitcalibration, focusing on the specific example of frequency errors which mayarise from fabrication variances or ambient magnetic fields. Our resultsdemonstrate that optimal interpolation techniques display near optimalerror-scaling in cases where the measured characteristic (here the qubitfrequency) varies smoothly, and we probe the limits of these benefits as afunction of measurement uncertainty. For more complex spatial variations, wedemonstrate that the NMQA formalism for adaptive measurement and noisefiltering outperforms optimal interpolation techniques in isolation, andcrucially, can be combined with insights from optimal interpolation theory toproduce a general purpose protocol.

Integration of spectator qubits into quantum computer architectures for hardware tuneup and calibration