We describe a new approach for quantum cosmology based on computational complexity. By defining a cosmology as a space-time containing a vacuum with specified properties (for example small cosmological constant) together with rules for how time evolution will produce the vacuum, we can associate global time in a multiverse with clock time on a supercomputer which simulates it. We argue for a principle of ``limited computational complexity" governing early universe dynamics as simulated by this supercomputer, which translates to a global measure for regulating the infinities of eternal inflation. We also give various definitions of the computational complexity of a cosmology, and argue that there are only a few natural complexity classes. Based on joint work with Frederik Denef, Brian Greene and Claire Zukowski, and the preprint arXiv:1706.06430 . |