Treespilation: architecture- and state-optimised fermion-to-qubit mappings

Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermionic problem in the qubits of a quantum computer. In this work, we introduce ‘Treespilation,’ a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings while minimising a generic cost function to reduce quantum simulation overhead. We use this technique to minimise the number of CNOT gates required to simulate approximate chemical groundstate circuits and observe significant reductions, up to 74%, in CNOT counts on full connectivity. For devices with limited qubit connectivity, we observe similar reductions in CNOT counts, often surpassing the full connectivity CNOT count for circuits encoded with the Jordan-Wigner mapping. We observed similar reductions when applied to reducing the Pauli weight of Hubbard model Hamiltonians.