  Diode is one of basic electronic components. It has a nonreciprocal current
response, associated with a broken space/time reversal symmetry. Here we
demonstrate prototypes of superconducting diodes operational at zero magnetic
field. They are based on conventional niobium planar Josephson junctions, in
which space/time symmetry is broken by a combination of self-field effect from
nonuniform bias and stray fields from a trapped Abrikosov vortex. We
demonstrate that nonreciprocity of critical current in such diodes can reach an
order of magnitude and rectification efficiency can exceed 70$\%$. Furthermore,
we can easily change the diode polarity and switch nonreciprocity on/off by
changing bias configuration and by trapping/removing a vortex. This facilitates
memory functionality. We argue that such diode-with-memory can be used for a
future generation of in-memory superconducting computers.
