Quantum channel simulation of phylogenetic branching models

Quantum channel simulations constructing probability tensors for biological multi-taxa in
phylogenetics are proposed. These are given in terms of positive trace preserving maps (quantum
channels), operating on quantum density matrices, using evolving systems of quantum walks with
multiple walkers. Simulation of a variety of standard phylogenetic branching models, applying on
trees of various topologies, is constructed using appropriate decoherent quantum circuits. For the
sequences of biological characters so modelled, quantum simulations of statistical inference for
them are constructed, given appropriate aligned molecular sequence data. This is achieved by the
introduction of a quantum pruning map, operating on likelihood operator observables, utilizing
state-observable duality and quantum measurement theory. More general stategies for related quantum
simulation targets are also discussed.

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