# 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.