Year: 2025
Type: article
Abstract: 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.
Source: Quantum
Authors: Maarten Stroeks, Barbara M. Terhal
Institutions: QuTech, Delft University of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Awards: G1665575404, G22081376, G490769153
OpenAlex ID: W4415729156