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Fermion-to-qubit mappings are used to represent fermionic modes on quantumcomputers, an essential first step in many quantum algorithms for electronicstructure calculations. In this work, we present a formalism to design flexiblefermion-to-qubit mappings from ternary trees. We discuss in an intuitive mannerthe connection between the generating trees' structure and certain propertiesof the resulting mapping, such as Pauli weight and the delocalisation of modeoccupation. Moreover, we introduce a recipe that guarantees Fock basis statesare mapped to computational basis states in qubit space, a desirable propertyfor many applications in quantum computing. Based on this formalism, weintroduce the Bonsai algorithm, which takes as input the potentially limitedtopology of the qubit connectivity of a quantum device and returns a tailoredfermion-to-qubit mapping that reduces the SWAP overhead with respect to otherparadigmatic mappings. We illustrate the algorithm by producing mappings forthe heavy-hexagon topology widely used in IBM quantum computers. The resultingmappings have a favourable Pauli weight scaling $\mathcal{O}(\sqrt{N})$ on thisconnectivity, while ensuring that no SWAP gates are necessary for singleexcitation operations.

The Bonsai algorithm: grow your own fermion-to-qubit mapping