Fermionic Hamiltonians without trivial low-energy states

Yaroslav Herasymenko; Anurag Anshu; Barbara Terhal; Jonas Helsen

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arXiv · 2307.13730

Fermionic Hamiltonians without trivial low-energy states

Yaroslav Herasymenko·Anurag Anshu·Barbara Terhal·Jonas Helsen

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Abstract

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]. We define a fermionic analogue of the class quantum PCP and discuss its relation with the qubit version.

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Yaroslav Herasymenko, Anurag Anshu, Barbara Terhal, Jonas Helsen. 2023-07-25. Fermionic Hamiltonians without trivial low-energy states. https://arxiv.org/abs/2307.13730

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