Fermionic Hamiltonians without trivial low-energy states

• URL: http://arxiv.org/abs/2307.13730v1
• Date: Tue, 25 Jul 2023 18:00:02 GMT
• Title: Fermionic Hamiltonians without trivial low-energy states
• Authors: Yaroslav Herasymenko, Anurag Anshu, Barbara Terhal, Jonas Helsen
• Abstract summary: We construct local fermionic Hamiltonians with no low-energy trivial states (NLTS) Distinctly from the qubit case, we define trivial states via finite-depth $textitfermionic$ quantum circuits. We define a fermionic analogue of the class quantum PCP and discuss its relation with the qubit version.
• Score: 12.961180148172197
• License: http://creativecommons.org/licenses/by/4.0/
• 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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