Integration of spectator qubits into quantum computer architectures for hardware tune-up and calibration

Performing efficient quantum computer tune-up and calibration is essential for growth in system complexity. In this work we explore the link between facilitating such capabilities and the underlying architecture of the physical hardware. We focus on the specific challenge of measuring (mapping) spatially inhomogeneous quasistatic calibration errors using spectator qubits dedicated to the task of sensing and calibration. We introduce an architectural concept for such spectator qubits: arranging them spatially according to prescriptions from optimal two-dimensional approximation theory. We show that this insight allows for efficient reconstruction of inhomogeneities in qubit calibration, focusing on the specific example of frequency errors which may arise from fabrication variances or ambient magnetic fields. Our results demonstrate that optimal interpolation techniques display near optimal error scaling in cases where the measured characteristic (here the qubit frequency) varies smoothly, and we probe the limits of these benefits as a function of measurement uncertainty. For more complex spatial variations, we demonstrate that the noise mapping for quantum architectures formalism for adaptive measurement and noise filtering outperforms optimal interpolation techniques in isolation and, crucially, can be combined with insights from optimal interpolation theory to produce a general purpose protocol.