Relatively recent results connected the study of quantum computation to the approximation of the value of the Jones polynomial of a braid at certain parameters. Specifically it was shown that a certain approximation was a complete problem for quantum computation: i.e. this problem captured the complete power of a quantum computer. More recently, work has shown a connection between quantum computation and the approximation of the Tutte polynomial that has a somewhat surprising “non-unitary” component to it. In this talk, we’ll present ongoing work that presents a quantum computer as an approximator of tensor networks. This geometric vision will be natural (for good reason) to those familiar with planar algebras or statistical physics models. We’ll connect this point of view to the previously mentioned results, point to new directions, and discuss natural questions that result. No specialized knowledge of any of the words mentioned above will be assumed.