  In the last years, we have been witnessing a tremendous push to demonstrate
that quantum computers can solve classically intractable problems. This effort,
initially focused on the hardware, progressively included the simplification of
the models to be simulated. We consider Hamiltonians written in terms of Pauli
operators and systematically cut all qubits that are not essential to simulate
the system. Our approach is universally applicable and lowers the complexity by
first ensuring that the largest possible portion of the Hilbert space becomes
irrelevant, and then by finding and exploiting all conserved charges of the
system, i.e., symmetries that can be expressed as Pauli operators. Remarkably,
both processes are classically efficient and optimal. To showcase our
algorithm, we simplify chemical molecules, lattice gauge theories, the Hubbard
and the Kitaev models.
