SQUIDs may detect local magnetic fields. SQUIDS of varying sizes, and hence sensitivities may detect different magnitudes of magnetic fields. SQUIDs may be oriented to detect magnetic fields in a variety of orientations, for example along an orthogonal reference frame of a chip or wafer. The SQUIDS may be formed or carried on the same chip or wafer as a superconducting processor (e.g., a superconducting quantum processor). Measurement of magnetic fields may permit compensation, for example allowing tuning of a compensation field via a compensation coil and/or a heater to warm select portions of a system. A SQIF may be implemented as a SQUID employing an unconventional grating structure. Successful fabrication of an operable SQIF may be facilitated by incorporating multiple Josephson junctions in series in each arm of the unconventional grating structure.