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We investigate models of nonlinear qubit evolution based on mappings to an$n$-qubit central spin model (CSM) in the large $n$ limit, where mean fieldtheory is exact. Extending a theorem of Erd\"os and Schlein, we establish thatthe CSM is rigorously dual to a nonlinear qubit when $n \rightarrow \infty$.The duality supports a type of nonlinear quantum computation in systems, suchas a condensate, where a large number of ancilla couple symmetrically to a"central" qubit. It also enables a gate-model implementation of nonlinearquantum simulation with a rigorous error bound. Two variants of the model, withand without coupling between ancilla, map to effective models with differentnonlinearity and symmetry. The duality discussed here might also be interestingfrom a quantum foundations perspective. There has long been interest in whetherquantum mechanics might possess some type of small, unobserved nonlinearity. Ifnot, what is the principle prohibiting it? The duality implies that there isnot a sharp distinction between universes evolving according to linear andnonlinear quantum mechanics: A one-qubit "universe" prepared in a pure state $|\varphi \rangle $ at the time of the big bang and symmetrically coupled toancilla prepared in the same state, would appear to evolve nonlinearly for anyfinite time $t>0$ as long as there are exponentially many ancilla $n \gg {\rmexp}(O(t))$.

The universe as a nonlinear quantum simulation: Large $n$ limit of the central spin model