Fermionic Hamiltonians without trivial low-energy states

• Published in: arXiv.org
• Main Authors: Herasymenko, Yaroslav, Anshu, Anurag, Terhal, Barbara, Helsen, Jonas
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.07.2023
• Subjects: Fermions; Qubits (quantum computing)

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.