Physicist here: yes, it is theoretically possible, but practically impossible because the complexity of a classical simulation of a quantum system scales exponentially in the physical size of the system.

It would be practically possible if the problem has useful symmetries, like only allowing 2-dimensional Hilbert spaces (qubits), and a set of possible transformations (e.g. Clifford+T gates) as we do in quantum computing. In fact one of the things we actually do that resembles what you are describing is quantum error correction, where codes are concatenated until the rate of logical errors becomes low enough.