Fermionic Gaussian Simulation: Applications and Beyond

We review existing classical simulation methods for performing fermionic Gaussian operations and develop new methods to address the gap by adhering to the fundamental theoretical framework established by Bravyi [Quantum Info. Comput. 5, 216 (2005)] for the most general fermionic Gaussian processes. Throughout this attempt, the focus remains on the unified approach that can be applied to generic fermionic Gaussian operations. This is beneficial since the selection of simulation methods has often been based on an ad hoc choice, heavily influenced by the specific model and circumstances, rather than on a systematic approach. Recently, an important step toward fermionic quantum computation has been reported on fermonic atoms on optical superlattice [2,3].

[1] Fang, Y., H. Choi, M. Lee, & M.-S. Choi, Advanced Quantum Technologies 9 (4), e00758 (2026). “Efficient Gaussian Simulations of Fermionic Open Quantum Systems”.

[2] Bojović, P., T. Hilker, S. Wang, et al., Nature 652 (8110), 602 (2026). “High-fidelity collisional quantum gates with fermionic atoms”.

[3] Kiefer, Y., Z. Zhu, L. Fischer, et al., Nature 652 (8110), 609 (2026). “Protected quantum gates using qubit doublons in dynamical optical lattices”.