  Optimal control of nanomagnets has become an urgent problem for the field of
spintronics as technological tools approach thermodynamically determined limits
of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding
optimal protocols is challenging, requiring detailed information about the
dynamical fluctuations of the controlled system. We provide a new, physically
transparent derivation of a metric tensor for which the length of a protocol is
proportional to its dissipation. This perspective simplifies nonequilibrium
optimization problems by recasting them in a geometric language. We then
describe a numerical method, an instance of geometric minimum action methods,
that enables computation of geodesics even when the number of control
parameters is large. We apply these methods to two models of nanomagnetic bits:
a simple Landau-Lifshitz-Gilbert description of a single magnetic spin
controlled by two orthogonal magnetic fields and a two dimensional Ising model
in which the field is spatially controlled. These calculations reveal
nontrivial protocols for bit erasure and reversal, providing important,
experimentally testable predictions for ultra-low power computing.
