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.