SKModel

class SKModel(num_sites, rng_or_seed=None)

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. :returns: A graph for a problem.

num_sites

Getter of the number of sites. :returns: Number of sites.

Methods

disorder()

Generate a new disorder of the SK model.

interpret(result)

Interpret a result as configuration of spins.

Parameters:

result (OptimizationResult | ndarray) – The calculated result of the problem.

Returns:

configuration of spins

Return type:

List[int]

static sample_most_likely(state_vector)

Compute the most likely binary string from state vector.

Parameters:

state_vector (QuasiDistribution | Statevector | ndarray | Dict) – state vector or counts or quasi-probabilities.

Returns:

binary string as numpy.ndarray of ints.

Raises:

ValueError – if state_vector is not QuasiDistribution, Statevector, np.ndarray, or dict.

Return type:

ndarray

to_quadratic_program()

Convert an SK model problem instance into a QuadraticProgram.

Returns:

The QuadraticProgram created from the SK problem instance.

Return type:

QuadraticProgram