Fermionic Hamiltonians without trivial low-energy states

Understand

We construct local fermionic Hamiltonians with no low-energy trivial states (NLTS), providing a fermionic counterpart to the NLTS theorem.

• Distinctly from the qubit case, we define trivial states via finite-depth $\textit{fermionic}$ quantum circuits.
• We furthermore allow free access to Gaussian fermionic operations, provided they involve at most $O(n)$ ancillary fermions.
• The desired fermionic Hamiltonian can be constructed using any qubit Hamiltonian which itself has the NLTS property via well-spread distributions over bitstrings, such as the construction in [Anshu, Breuckmann, Nirkhe, STOC 2023].