SKModel¶

class SKModel(num_sites, rng_or_seed=None)[source]¶

Bases: OptimizationApplication

Optimization application of the “Sherrington Kirkpatrick (SK) model” [1].

The SK Hamiltonian over n spins is given as: \(H(x)=-1/\sqrt{n} \sum_{i<j} w_{i,j}x_ix_j\), where \(x_i\in\{\pm 1\}\) is the configuration of spins and \(w_{i,j}\in\{\pm 1\}\) is a disorder chosen independently and uniformly at random. Notice that there are other variants of disorders e.g., with \(w_{i,j}\) chosen from the normal distribution with mean 0 and variance 1.

References

[1]: Dmitry Panchenko. “The Sherrington-Kirkpatrick model: an overview”, https://arxiv.org/abs/1211.1094

Parameters:

num_sites (int) – number of sites
rng_or_seed (Generator | int | None) – NumPy pseudo-random number generator or seed for np.random.default_rng(<seed>) or None. None results in usage of np.random.default_rng().

Attributes

`graph`	Getter of the graph representation.
`num_sites`	Getter of the number of sites.

Methods

`disorder`()	Generate a new disorder of the SK model.
`interpret`(result)	Interpret a result as configuration of spins.
`to_quadratic_program`()	Convert an SK model problem instance into a `QuadraticProgram`.