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We detail techniques to optimise high-level classical simulations of Shor'squantum factoring algorithm. Chief among these is to examine the entanglingproperties of the circuit and to effectively map it across the one-dimensionalstructure of a matrix product state. Compared to previous approaches whosespace requirements depend on $r$, the solution to the underlying order-findingproblem of Shor's algorithm, our approach depends on its factors. We performeda matrix product state simulation of a 60-qubit instance of Shor's algorithmthat would otherwise be infeasible to complete without an optimisedentanglement mapping.

Optimising Matrix Product State Simulations of Shor's Algorithm