# Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

• Sam McArdle
• Earl Campbell
• Yuan Su
Phys. Rev. A, vol. 105 (2022), pp. 012403

## Abstract

Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number information in the implementation of Trotter-based approach and overestimated the quantum-computer runtime as a result. They also depended on numerical procedures that are computationally too expensive to scale up to large systems of practical interest. Here we propose techniques that solve both problems by using various factorized decompositions of the electronic structure Hamiltonian. We showcase our techniques for the uniform electron gas, finding substantial (over $100\times$) improvements in Trotter error for low-filling fraction and pushing to much higher numbers of orbitals than is possible with existing methods. Finally, we calculate the $T$-count to perform phase-estimation on Jellium. In the low-filling regime, we observe improvements in gate complexity of over $10\times$ compared to the best Trotter-based approach reported to date. We also report gate counts competitive with qubitization-based approaches for Wigner-Seitz values of physical interest.