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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.15368 |
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| _version_ | 1866929724200058880 |
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| author | Anand, Kartik |
| author_facet | Anand, Kartik |
| contents | Quantum PCP conjecture is one of the most influential open problems in quantum complexity theory, which states that approximating the ground state energy for a sparse local Hamiltonian upto a constant is QMA-complete. However, even though the problem remains unsolved, weaker versions of it-such as the NLTS [FH13, ABN22] and NLSS [GG22] conjectures-have surfaced in the hope of providing evidence for QPCP. While the NLTS hamiltonians were first constructed in[ABN22], NLSS conjecture still remains unsolved. Weaker versions of the NLSS conjecture were addressed in [CCNN23, CCNN24], demonstrating that Clifford and almost-Clifford states-a subclass of sampleable states-have a lower energy bound on Hamiltonians prepared by conjugating the NLTS Hamiltonians from [ABN22]. In similar spirit, we construct a class of fermionic Hamilltonians for which energy of Gaussian states, a subclass of sampleable fermionic states, is bounded below by a constant. We adapt the technique used in [CCNN23] to our context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Fermionic Hamiltonians with Non-Gaussianic low-energy states Anand, Kartik Quantum Physics Quantum PCP conjecture is one of the most influential open problems in quantum complexity theory, which states that approximating the ground state energy for a sparse local Hamiltonian upto a constant is QMA-complete. However, even though the problem remains unsolved, weaker versions of it-such as the NLTS [FH13, ABN22] and NLSS [GG22] conjectures-have surfaced in the hope of providing evidence for QPCP. While the NLTS hamiltonians were first constructed in[ABN22], NLSS conjecture still remains unsolved. Weaker versions of the NLSS conjecture were addressed in [CCNN23, CCNN24], demonstrating that Clifford and almost-Clifford states-a subclass of sampleable states-have a lower energy bound on Hamiltonians prepared by conjugating the NLTS Hamiltonians from [ABN22]. In similar spirit, we construct a class of fermionic Hamilltonians for which energy of Gaussian states, a subclass of sampleable fermionic states, is bounded below by a constant. We adapt the technique used in [CCNN23] to our context. |
| title | Constructing Fermionic Hamiltonians with Non-Gaussianic low-energy states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.15368 |