# Computational complexity of the Rydberg blockade in two dimensions

@article{Pichler2018ComputationalCO, title={Computational complexity of the Rydberg blockade in two dimensions}, author={Hannes Pichler and Sheng-Tao Wang and Leo Zhou and Soonwon Choi and Mikhail D. Lukin}, journal={ArXiv}, year={2018}, volume={abs/1809.04954} }

We discuss the computational complexity of finding the ground state of the two-dimensional 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 so-called Rydberg blockade mechanism. We show that the solution to NP-complete…

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## References

SHOWING 1-10 OF 22 REFERENCES

### Computers and Intractability: A Guide to the Theory of NP-Completeness

- Computer Science
- 1978

The experiences, understandings, and beliefs that guide the professional practices of teacher educators are explored, and the book paints a picture of a profession that offers huge rewards, alongside challenges and frustrations.

### Physical Review A 98

- 1151
- 2018

### Discrete Mathematics 86

- 165
- 1990

### Physical Review X 8

- 021069
- 2018

### Nature 473

- 194
- 2011

### Science 295

- 2427
- 2002

### Any choice of q works, as long as we choose 2φ < 2q ≤ k/4 and q ∼ O(k)

### Science 354

- 1024
- 2016