Quantum channel simulation of phylogenetic branching models. (English) Zbl 1507.81060
Summary: 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.
MSC:
| 81P47 | Quantum channels, fidelity |
| 94A40 | Channel models (including quantum) in information and communication theory |
| 81P68 | Quantum computation |
| 68Q12 | Quantum algorithms and complexity in the theory of computing |
Keywords:
quantum algorithms; quantum channels; quantum walks; quantum biology; open quantum systems; mathematical phylogeneticsSoftware:
RAxMLReferences:
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