Reduced Entanglement Requirements in Fermionic Simulation Through Fermion-To-Qubit Mapping Optimization

Abstract

In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a novel method for deriving optimized mappings that significantly reduce the entanglement requirements for prepared states of interest. The presence of single and double electronic excitations drives the optimization of the mapping, greatly simplifying correlations for target states in the qubit space. Additionally, the code implementation for designing arbitrary ternary tree mappings in the Tequila Python library is provided. Enhanced simulation accuracy is validated on the optimized mappings both in quantum computing, using the variational quantum eigensolver, and in tensor networks by employing density matrix renormalization group on a matrix product state.