  Simulating quantum systems constructively furthers our understanding of
qualitative and quantitative features which may be analytically intractable. In
this letter, we directly simulate and explore the entanglement structure
present in a paradigmatic example of quantum information: Shor's wavefunction.
The methodology employed is a dynamical tensor network which is initially
constructed as a tree tensor network, inspired by the modular exponentiation
quantum circuit, and later efficiently mapped to a matrix product state.
Utilizing the Schmidt number as a local entanglement metric, our construction
explicitly captures the wavefunction's non-local entanglement structure and an
entanglement scaling relation is discovered. Specifically, we see that
entanglement across a bipartition grows exponentially in the number of qubits
before saturating at a critical scale which is proportional to the modular
periodicity.
