Quadratic terms of input spin glass have flipped quadratic energy (bug)

[yannick-couzinie]

Hey, thanks for providing this code. To get it to compile I had to make some changes to the cmake file and I had to switch to the master branch on the pybind11 module, but I managed to get it compiled.

I then take the following file

import siquan
dtsqa = siquan.DTSQA()
dtsqa.setHSchedule("[10,iF,0.01]")
dtsqa.setTSchedule("[0.01, 0.01]")

resultDict = dtsqa.minimize( [(-0.1, [0]), (-0.01, [1]), (-0.001, [2]),  (1.5, [0,1]), (1., [0, 1, 2])],  3)

which, if I understand correctly, corresponds to finding the minimum energy of a spin glass -1 s1 - 0.01 s2 - 0.001 s3 + 1.5 s1*s2 + s1*s2*s3 where si can take values of +1 or -1. The resulting resultDict is

{'H': '[10, iF, 0.01]',
 'T': '[0.01,  0.01]',
 'energy': '-2.609000',
 'energy_distr': '{0: -2.609, 1: -0.109, 2: -1.5, 3: -1}',
 'first_in': '0',
 'maxcut': '0.110000',
 'nt': '100',
 'periodic': '1',
 'remap': 'sorted,fill,0',
 'runtime_cycles': '9018166',
 'runtime_sec': '0.009023',
 'seed': '0',
 'state': '[2]',
 'steps': '1000',
 'trotter_degen': '54',
 'trotter_min_index': '0'}

I struggle to understand this output. Following the linear energies (resultDict['energy_distr'][1]) it is apparent that s1=1, s2=1 and s3=-1 to get -0.1-0.01+0.001=-0.109. This would also agree with resultDict['state'] if we assume that it gives a list of spins that are -1 in the output (here 2, i.e. the third spin). For the quadratic term resultDict['energy_distr'][2]=-1.5 we need s1*s2 = -1 to get the contribution of 1.5.s1*s2=-1.5, which violates what we found for the linear term, for the cubic term resultDict['energy_distr'][3]=-1 we need s1*s2*s3 = -1 which agrees with the linear term if we take s1 = s2 = -s3 = 1.

Running some of these smaller experiments it seems like the quadratic terms in the spin glass are multiplied by -1 in the optimization so that for example for the above example we optimized -1 s1 - 0.01 s2 - 0.001 s3 - 1.5 s1*s2 + s1*s2*s3 and not the original input.

Am I misunderstanding the way to use this library or is this a bug?