  Recent studies of genotype-phenotype (GP) maps have reported universally
enhanced phenotypic robustness to genotype mutations, a feature essential to
evolution. Virtually all of these studies make a simplifying assumption that
each genotype maps deterministically to a single phenotype. Here, we introduce
probabilistic genotype-phenotype (PrGP) maps, where each genotype maps to a
vector of phenotype probabilities, as a more realistic framework for
investigating robustness. We study three model systems to show that our
generalized framework can handle uncertainty emerging from various physical
sources: (1) thermal fluctuation in RNA folding, (2) external field disorder in
spin glass ground state finding, and (3) superposition and entanglement in
quantum circuits, which are realized experimentally on a 7-qubit IBM quantum
computer. In all three cases, we observe a novel biphasic robustness scaling
which is enhanced relative to random expectation for more frequent phenotypes
and approaches random expectation for less frequent phenotypes.
