Twisted quantum doubles are sign problem-free

The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be realized in a local sign problem-free Hamiltonian due to the non-positivity of the wavefunction. We show that this is not the case. Despite failing to be stoquastic - the standard criteria for the existence of a sign problem - the double semion model as well as all twisted quantum double phases of matter for finite groups G can be realized in local sign problem-free Hamiltonians. The lack of a sign problem is not fine-tuned and does not require the Hamiltonian to be exactly solvable, with sign problem-free perturbations allowing access to a variety of topological phase transitions.