  Superconducting materials with non-centrosymmetric lattices lacking the space
inversion symmetry are known to exhibit a variety of interesting
parity-breaking phenomena, including the anomalous Josephson effect. Here we
consider a Josephson junction consisting of two non-centrosymmetric
superconductors (NCSs) connected by a uniaxial ferromagnet, and demonstrate
that it exhibits a direct analog of the Chiral Magnetic Effect observed in
Dirac and Weyl semimetals. We propose to use this "Chiral Magnetic Josephson
junction" (CMJ junction) as an element of a qubit with a Hamiltonian tunable by
the ferromagnet's magnetization. The CMJ junction allows to avoid the use of an
offset magnetic flux in inductively shunted qubits, thus enabling a simpler and
more robust architecture. The resulting"`chiral magnetic qubit" is protected
from the noise caused by fluctuations in magnetization when the easy axis of
the uniaxial ferromagnet is directed across the junction.
