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We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an -mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than qubits on average. We apply it to the problem of learning -fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that one can determine individual elements of all -fermion RDMs in parallel, to precision , by repeating a single quantum circuit for times. This result is based on a method we develop here that allows one to determine individual elements of all -qubit RDMs in parallel, to precision , by repeating a single quantum circuit for times, independent of the system size. This improves over existing schemes for determining qubit RDMs.