Solomonoff induction is about putting probability distributions on observations - you're looking for the combination of the simplest program that puts the highest probability on observations. Technically, the original SI doesn't talk about causal models you're embedded in, just programs that assign probabilities to experiences.

Generalizing somewhat, for QM as it appears to humans, the generalized-SI-selected hypothesis would be something along the lines of one program that extrapolated the wavefunction, then another program that looked for people inside it and translated the underlying physics into the "observed data" from their perspective, then put probabilities on the sequences of data corresponding to integral squared modulus. Note that you also need an interface from atoms to experiences just to e.g. translate a classical atomic theory of matter into "I saw a blue sky", and an implicit theory of anthropics/sum-probability-measure too if the classical universe is large enough to have more than one copy of you.