  Topological qubits composed of unpaired Majorana zero-modes are under intense
experimental and theoretical scrutiny in efforts to realize practical quantum
computation schemes. In this work, we show the minimum four \textit{unpaired}
Majorana zero-modes required for a topological qubit according to braiding
schemes and control of entanglement for gate operations are inherent to
multiplicative topological phases, which realize symmetry-protected tensor
products -- and maximally-entangled Bell states -- of unpaired Majorana
zero-modes known as multiplicative Majorana zero-modes. We introduce
multiplicative Majorana zero-modes as topologically-protected boundary states
of both one and two-dimensional multiplicative topological phases, using
methods reliant on multiplicative topology to construct relevant Hamiltonians
from the Kitaev chain model. We furthermore characterize topology in the bulk
and on the boundary with established methods while also introducing techniques
to overcome challenges in characterizing multiplicative topology. In the
process, we explore the potential of these multiplicative topological phases
for an alternative to braiding-based topological quantum computation schemes,
in which gate operations are performed through topological phase transitions.
