Pruned Histories and the Computational Multiverse: What Does Quantum Speedup Ontologically Require?

Deutsch's influential argument holds that the exponential speedup of quantum algorithms such as Shor's is best explained by computation distributed across ontologically real parallel branches of the wavefunction. This paper interrogates that claim by asking what minimal ontological commitments are actually required to underwrite observed quantum computational advantages. Drawing on the framework of final-state constraints and informational pruning developed in prior work, we argue that Deutsch's computational argument depends on an unpruned Everettian ontology in which all branches persist as computational substrates. We show that pruned-histories interpretations—in which boundary conditions or decoherence-based selection mechanisms restrict the space of ontologically realized branches—can preserve the empirical predictions of quantum computation while denying the parallel-universes inference. The argument requires three positive commitments: a records-based criterion for ontological commitment, a thermodynamically graded boundary between unitary computation and outcome-stabilization, and a positive account of computational speedup grounded in global Hilbert-space structure and entanglement rather than in a population of parallel worlds. We situate this result within the ontological models framework and recent observer-dependence theorems—including Frauchiger-Renner, Bong et al., and Walleghem et al.—and engage directly with Hewitt-Horsman's functionalist defense of computational branch realism. We conclude that the Deutsch argument, while rhetorically powerful, is interpretation-laden rather than interpretation-neutral.