Two Slightly-Entangled NP-Complete Problems

Details Two Slightly-Entangled NP-Complete Problems Two Slightly-Entangled NP-Complete Problems

2005-02-02

arxiv.org/abs/quant-ph/0502022v1

Quantum Information and Computation, Vol. 5, No. 6 (2005), pp. 449-455

Physics

Quantum Physics

5 pages

Scientific paper

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.

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