anti_crossing_loops(num_variables: int) BinaryQuadraticModel[source]#

Generate an anti-crossing problem with two loops.

The low-energy space of this model consists of a unique ground state of all \(+1\)s and a degenerate first excited state, centered at all \(-1\)s, with these two lowest states well separated in Hamming distance and by an energy barrier. These features are sufficient to yield a small anti-crossing when employed in a transverse-field annealing process. A closely related approach is employed in [DJA].

Note that for small values of num_variables, the loops can be as small as a single edge.


num_variables – Number of variables used to generate the problem. Must be an even number greater than or equal to 8.


A binary quadratic model.


Dickson, N., Johnson, M., Amin, M. et al. Thermally assisted quantum annealing of a 16-qubit problem. Nat Commun 4, 1903 (2013). https://doi.org/10.1038/ncomms2920