Magnetic field calculations in the vicinity of superconductive circuit structures

Modeling the magnetic field generated by currents in thin-film superconducting structures is useful to a broad range of applications. Present methods calculate the magnetic field around such structures from two-dimensional current sheets. We present an efficient and accurate algorithm to calculate the magnetic field at arbitrary locations in three dimensions, both internal and external to the structures. We use a combination of FastHenry and InductEx to calculate the current density, from which we compute the magnetic field semi-analytically using Biot-Savart's law. As practical examples, we employ the algorithm to compute (i) the mean square flux noise in square SQUID and qubit loops and (ii) the dc bias current-induced magnetic field in real digital circuit layouts.