Optimising Matrix Product State Simulations of Shors Algorithm

We detail techniques to optimise high-level classical simulations of Shors quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shors algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shors algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.