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: Shors 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 wavefunctions 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.
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