  Memristors, memcapacitors, and meminductors, collectively called memelements,
represent an innovative generation of circuit elements whose properties depend
on the state and history of the system. The hysteretic behavior of one of their
constituent variables, under the effect of an external time-dependent
perturbation, is their distinctive fingerprint. In turn, this feature endows
them with the ability to both store and process information on the same
physical location, a property that is expected to benefit many applications
ranging from unconventional computing to adaptive electronics to robotics, to
name just a few. For all these types of applications, it is important to find
appropriate memelements that combine a wide range of memory states (multi-state
memory), long memory retention times, and protection against unavoidable noise.
Although several physical systems belong to the general class of memelements,
few of them combine all of these important physical features in a single
component. Her we demonstrate theoretically a superconducting memory structure
based on solitonic long Josephson junctions (LJJs). We show that the Josephson
critical current of the junction behaves hysteretically as an external magnetic
field is properly swept. According to the hysteretic path displayed by the
critical current, a LJJ can be used as a multi-state memory, with a
controllable number of available states. In addition, since solitons are at the
core of its operation, this system provides an intrinsic topological protection
against external perturbations. Solitonic Josephson-based memelements may find
applications as memories, and in other emerging areas such as memcomputing,
i.e., computing directly in/by the memory.
