  Merons and skyrmions are classical topological solitons. However, they will
become quantum mechanical objects when their sizes are of the order of
nanometers. Recently, quantum computation based on nanoscale skyrmions was
proposed. Here, we propose to use a nanoscale meron in a magnetic nanodisk as a
qubit, where the up and down directions of the core spin are assigned to be the
qubit states $|0\rangle$ and $|1\rangle$. First, we show numerically that a
meron with the radius containing only $7$ spins can be stabilized in a
ferromagnetic nanodisk classically. Then, we show theoretically that universal
quantum computation is possible based on merons by explicitly constructing the
arbitrary phase-shift gate, the Hadamard gate, and the CNOT gate. They are
executed by magnetic field or electric current. It would serve as a qubit with
long coherence time as a remnant of topological stability from its classical
counterpart.
