SMT Generation¶

generate
(graph, feasible_configurations, decision_variables, linear_energy_ranges, quadratic_energy_ranges, min_classical_gap, smt_solver_name=None)[source]¶ Generates the Ising model that induces the given feasible configurations. The code is based on the papers 1 and 2.
 Parameters
graph (nx.Graph) – The target graph on which the Ising model is to be built.
feasible_configurations (dict) – The set of feasible configurations of the decision variables. The key is a feasible configuration as a tuple of spins, the values are the associated energy.
decision_variables (list/tuple) – Which variables in the graph are assigned as decision variables.
linear_energy_ranges (dict, optional) – A dict of the form {v: (min, max), …} where min and max are the range of values allowed to v.
quadratic_energy_ranges (dict) – A dict of the form {(u, v): (min, max), …} where min and max are the range of values allowed to (u, v).
min_classical_gap (float) – The minimum energy gap between the highest feasible state and the lowest infeasible state.
smt_solver_name (str/None) – The name of the smt solver. Must be a solver available to pysmt. If None, uses the pysmt default.
 Returns
A 4tuple containing:
dict: The linear biases of the Ising problem.
dict: The quadratic biases of the Ising problem.
float: The classical energy gap between ground and the first excited state.
 Return type
 Raises
ImpossiblePenaltyModel – If the penalty model cannot be built. Normally due to a nonzero infeasible gap.
 1
Bian et al., “Discrete optimization using quantum annealing on sparse Ising models”, https://www.frontiersin.org/articles/10.3389/fphy.2014.00056/full
 2
Z. Bian, F. Chudak, R. Israel, B. Lackey, W. G. Macready, and A. Roy “Mapping constrained optimization problems to quantum annealing with application to fault diagnosis” https://arxiv.org/pdf/1603.03111.pdf