The Bonsai algorithm: grow your own fermion-to-qubit mapping
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. Based on this formalism, we
introduce the Bonsai algorithm, which takes as input the potentially limited
topology of the qubit connectivity of a quantum device and returns a tailored
fermion-to-qubit mapping that reduces the SWAP overhead with respect to other
paradigmatic mappings. We illustrate the algorithm by producing mappings for
the heavy-hexagon topology widely used in IBM quantum computers. The resulting
mappings have a favourable Pauli weight scaling $\mathcal{O}(\sqrt{N})$ on this
connectivity, while ensuring that no SWAP gates are necessary for single
excitation operations.
Aaron Miller Zoltán Zimborás Stefan Knecht Sabrina Maniscalco Guillermo García-Pérez