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

Understand

Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations.

• In this work, we present a formalism to design flexible fermion-to-qubit mappings from ternary trees.
• We discuss in an intuitive manner the connection between the generating trees' structure and certain properties of the resulting mapping, such as Pauli weight and the delocalisation of mode occupation.
• Moreover, we introduce a recipe that guarantees Fock basis states are mapped to computational basis states in qubit space, a desirable property for many applications in quantum computing.