Feasibility and Optimal Strategies for Near-Term Simulations of Fermionic Systems

As quantum computing hardware continues to improve, several experiments have demonstrated the feasibility of simulating the properties of fermionic systems on near-term devices by employing Quantum Error Mitigation (QEM)[1,2]. However, the question of what combination of Fermion-to-Qubit mapping and QEM to utilize will depend on the size of the system of interest and quality of the hardware[3,4]. To facilitate the utility of such algorithms, we present a novel QEM technique, specifically tailored to fermionic simulation algorithms, which outperforms other widely used techniques such as Symmetry Verification, Virtual Distillation, and Probabilistic Error Cancellation [5] in regimes of practical interest. We then study the performance of different combinations of QEM and Fermion-to-Qubit mappings and identify the best combination depending on the available gate fidelities, number of shots, and size and dimensionality of the fermionic system. This study also enables us to derive minimal hardware requirements and analyze the prospects for the simulation of Fermi-Hubbard models of various sizes in near-term devices.

[1] Google Quantum AI, Science 369, 6507 (2020)

[2] Google Quantum AI, Nature 612, 240 (2022)

[3] R. W. Chien et al., arXiv:2303.02270 (2023)

[4] M. G. Algaba et al., Quantum 8, 1327 (2024)

[5] Z. Cai et al., Rev. Mod. Phys. 95, 045005 (2023)