  Tensor networks impose a notion of geometry on the entanglement of a quantum
system. In some cases, this geometry is found to reproduce key properties of
holographic dualities, and subsequently much work has focused on using tensor
networks as tractable models for holographic dualities. Conventionally, the
structure of the network - and hence the geometry - is largely fixed a priori
by the choice of tensor network ansatz. Here, we evade this restriction and
describe an unbiased approach that allows us to extract the appropriate
geometry from a given quantum state. We develop an algorithm that iteratively
finds a unitary circuit that transforms a given quantum state into an
unentangled product state. We then analyze the structure of the resulting
unitary circuits. In the case of non-interacting, critical systems in one
dimension, we recover signatures of scale invariance in the unitary network,
and we show that appropriately defined geodesic paths between physical degrees
of freedom exhibit known properties of a hyperbolic geometry.
