Complexity of Fermionic 2-SAT
| Autor: | Stroeks, Maarten, Terhal, Barbara M. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the fermionic satisfiability problem, Fermionic $k$-SAT: this is the problem of deciding whether there is a fermionic state in the null-space of a collection of fermionic, parity-conserving, projectors on $n$ fermionic modes, where each fermionic projector involves at most $k$ fermionic modes. We prove that this problem can be solved efficiently classically for $k=2$. In addition, we show that deciding whether there exists a satisfying assignment with a given fixed particle number parity can also be done efficiently classically for Fermionic 2-SAT: this problem is a quantum-fermionic extension of asking whether a classical 2-SAT problem has a solution with a given Hamming weight parity. We also prove that deciding whether there exists a satisfying assignment for particle-number-conserving Fermionic 2-SAT for some given particle number is NP-complete. Complementary to this, we show that Fermionic 9-SAT is QMA$_1$-hard. Comment: Fixed abstract for v2 |
| Databáze: | arXiv |
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