  We consider the surface states of a spherical topological insulator
piecewise-terminated by superconductivity or ferromagnetism over various
regions of the spherical surface. Such terminations gap the surface states by
breaking U(1) particle-number symmetry or time-reversal symmetry, respectively.
Interfaces and trijunctions between differently terminated surface regions can
host propagating and bound Majorana modes, and the finite size of the spherical
system makes it easily amenable to numerical analysis via exact diagonalization
of the Bogoliubov-de Gennes Hamiltonian within a truncated Hilbert space.
Creative termination patterning therefore allows one to prototype a variety of
Majorana circuits, calculating energy spectra and plotting eigenfunctions over
the spherical surface. We develop the computational framework for this
approach, establishing a virtual breadboard for Majorana circuitry, and apply
it to circuits of interest, including the Majorana analog of a Mach-Zehnder
interferometer.
