A lot of work has gone into looking for classical algorithms for these sampling problems since the mid-2000s, and we have found some speedups, but everything st

A lot of work has gone into looking for classical algorithms for these sampling problems since the mid-2000s, and we have found some speedups, but everything still suggests that they are truly exponential on classical hardware. The classical algorithms for these problems don't involve modeling qubits directly, but they do involve sampling exponentially many states and averaging over the results, which is a lot like modeling qubits.