Two slightly-entangled NP-complete problems (pp449-455)
         Roman Orus
          doi: https://doi.org/10.26421/QIC5.6-3
Abstracts: We perform a mathematical analysis of the classical computational complexity of two genuine quantum-mechanical problems, which are inspired in the calculation of the expected magnetizations and the entanglement between subsystems for a quantum spin system. These problems, which we respectively call SES and SESSP, are specified in terms of pure slightly-entangled quantum states of $n$ qubits, and rigorous mathematical proofs that they belong to the NP-Complete complexity class are presented. Both SES and SESSP are, therefore, computationally equivalent to the relevant $3$-SAT problem, for which an efficient algorithm is yet to be discovered.
Key words: entanglement, NP-complete, complexity theory