Computational complexity of the Rydberg blockade in two dimensions
Abstract
We discuss the computational complexity of finding the ground state of the twodimensional array of quantum bits that interact via strong van der Waals interactions. Specifically, we focus on systems where the interaction strength between two spins depends only on their relative distance $x$ and decays as $1/x^6$ that have been realized with individually trapped homogeneously excited neutral atoms interacting via the socalled Rydberg blockade mechanism. We show that the solution to NPcomplete problems can be encoded in ground state of such a manybody system by a proper geometrical arrangement of the atoms. We present a reduction from the NPcomplete maximum independent set problem on planar graphs with maximum degree three. Our results demonstrate that computationally hard optimization problems can be naturally addressed with coherent quantum optimizers accessible in near term experiments.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.04954
 Bibcode:
 2018arXiv180904954P
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases;
 Computer Science  Computational Complexity;
 Physics  Atomic Physics
 EPrint:
 12 pages, see also companion paper arXiv:1808.10816