Abstract
Matched instances of the quantum satisfiability problem have the following property: They have a product state solution. This is a mere existential statement and the problem is to find such a solution efficiently. Recent work by Gharibian and coauthors has made first progress on this question: They give an efficient algorithm which works for instances whose interaction hypergraph is restricted in a certain way.
We continue this line of research and give two results: First, an efficient algorithm is presented which works when the constraints themselves are restricted (the interaction hypergraph is not restricted). The restriction is that each constraint has at most 2 additive terms. Second, over the field of real numbers the problem of solving matched instances of QSat by product state solutions becomes NP-hard.
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Goerdt, A. (2019). Matched Instances of Quantum Satisfiability (QSat) – Product State Solutions of Restrictions. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_14
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DOI: https://doi.org/10.1007/978-3-030-19955-5_14
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