get_exp_vals

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get_exp_vals#

iqm.qaoa.tree_calculation.tree_calculation.get_exp_vals(p, big_d, h, big_gamma, big_beta, basis_list_t=None)#

Calculates the expectation values of <Z> and <ZZ> terms.

Basically, this reproduces the full calculation in equations A41-A44 and A49. The sum in equation A43 over \(t_a>t_b\) is split in two cases, \(t_b = 0\) and \(t_b > 0\).

Parameters:

  • p (int) – The number of QAOA layers, corresponding to the largest order of the fixed points that we want to calculate.

  • big_d (int) – Graph regularity minus one. Note that in expressions with \(\gamma\), we use \(\sqrt{D}\) in the denominator instead of \(\sqrt{d} = \sqrt{D+1}\), but this just introduces a small factor to the gamma angles.

  • h (float) – The local field of the problem.

  • big_gamma (ndarray) – The array of the \(\gamma\) angles of the QAOA. The full array, with a 0 in the middle (see A8).

  • big_beta (ndarray) – The array of the \(\beta\) angles of the QAOA. The full array, with a 0 in the middle (see A8).

  • basis_list_t (None | list[list[ndarray]]) – For some compatibility, the basis list sorted by the symmetry sectors can be pregenerated and given as an input. Otherwise it’s generated internally.

Returns:

A tuple of two floats representing the expectation values of <Z> and <ZZ> respectively. The output values are typed as np.complex128, but they are in fact real values (so their imaginary component is minimal).

Return type:

tuple[complex128, complex128]

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