Recent experimental advances in the field of cold atoms led to the
development of novel techniques for producing synthetic dimensions and
synthetic magnetic fields, thus greatly expanding the utility of cold atomic
systems for exploring exotic states of matter. In this paper we investigate
the possibility of using experimentally tunable interactions in such systems
to mimic the physics of Majorana chains, currently a subject of intense
research. Crucially to our proposal, the interactions, which are local in
space, appear non-local in the synthetic dimension. We use this fact to
induce coupling between counter-propagating edge modes in the quantum Hall
regime. For the case of attractive interactions in a system composed of two
tunneling-coupled chains, we find a gapless quasi-topological phase with a
doubly-degenerate ground state. While the total number of particles in the
system is kept fixed, this phase is characterized by strong fluctuations of
the pair number in each chain. Each ground state is characterized by the
parity of the total particle number in each chain, similar to Majorana wires.
However, in our system this degeneracy persists for periodic boundary
conditions. For open boundary conditions there is a small splitting of this
degeneracy due to the single-particle hopping at the edges. We show how
subjecting the system to additional synthetic flux or asymmetric potentials
on the two chains can be used to control
this nonlocal qubit.  We propose experimental probes for testing the nonlocal
nature of such a qubit and measuring its state.