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 Fermioinc 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
previously introduced by some of the authors. We use this technique to minimise
the number of CNOT gates required to simulate chemical groundstates found
numerically using the ADAPT-VQE algorithm. We observe significant reductions,
up to $74\%$, in CNOT counts on full connectivity and for limited qubit
connectivity-type devices such as IBM Eagle and Google Sycamore, we observe
similar reductions in CNOT counts. In many instances, the reductions achieved
on these limited connectivity devices even surpass the initial full
connectivity CNOT count. Additionally, we find our method improves the CNOT and
parameter efficiency of QEB- and qubit-ADAPT-VQE, which are, to our knowledge,
the most CNOT-efficient VQE protocols for molecular state preparation.
Aaron Miller Adam Glos Zoltán Zimborás