01600nas a2200145 4500008004100000245005700041210005700098260001500155490000800170520117800178100002101356700002401377700001601401856003701417 2017 eng d00aExtracting entanglement geometry from quantum states0 aExtracting entanglement geometry from quantum states c2017/10/060 v1193 a
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.
1 aHyatt, Katharine1 aGarrison, James, R.1 aBauer, Bela uhttps://arxiv.org/abs/1704.01974