  I present a novel way of linking the shift in the axion mass due to
non-perturbative gravitational effects and the quantum information
interpretation of the holographic principle. The main result of this article is
a novel way of expressing the shift in the axion mass by means of properties of
the tensor network used in the construction of the quantum information
interpretation of the holographic principle. Indeed it appears that the axion
mass shift can be seen as a geometric property of the holographic bulk
entanglement. Moreover, the explicit breaking of the continuous Peccei-Quinn
symmetry by gravitational instantons can be regarded as a result of including
tensors encoding gauge fields on the holographic bulk tensor network.
