dwave.system.temperatures.background_susceptibility_ising

background_susceptibility_ising(h: ndarray | dict, J: ndarray | dict) → Tuple

Create the field and couplings for the background susceptibility correction.

Background susceptibility is a significant source of systematic error in annealing processors, it can be treated as a perturbation of the programmed Hamiltonian.

The perturbed Hamiltonian can be most concisely expressed for an Ising model in matrix vector notation. Assuming J is a real symmetric (0 on diagonal) matrix, h and s are column vectors, and chi is a small real value, then the Ising model is is defined: \(H = k + (h + \chi J h)' s + 1/2 s' (J + \chi J^2) s\) ‘ denotes transpose and matrix multiplication applies. The constant (k, irrelevant to sampled distributions) is defined \(k = - \chi/2 Trace[J^2]\) This function returns the perturbative part \(H(s) = k + h' J s + 1/2 s' (J + \chi J^2) s\)

Parameters:

• h – linear terms (fields) in the Hamiltonian.

• J – quadratic terms (couplings) in the Hamiltonians

Returns:

A Tuple of fields, couplings and scalar constant. If h and J are of type np.ndarray so are returned fields and couplings. Otherwise a tuple of dictionaries is returned.

https://docs.dwavesys.com/docs/latest/c_qpu_ice.html#qpu-ice-background-susceptibility (accessed October 21, 2024)