SYSTEMS AND METHODS OF FINDING QUANTUM BINARY OPTIMIZATION PROBLEMS

1 . A method of problem solving on one or more processors, the method comprising:

receiving a relation and a graph;

initializing a probe set;

initializing a lower bound;

for a number of cycles until an end condition is reached:

iterating over an expansion of the probe set and a configuration of helper variables to solve a first linear program for a quadratic unconstrained binary optimization (QUBO) problem and an energy gap which corresponds to the QUBO problem;

selecting an expanded probe set with a sufficiently small number of solutions for which the energy gap exceeds the lower bound;

determining whether there are no solutions for which the energy gap exceeds the lower bound,

in response to determining that there are no solutions for which the energy gap exceeds the lower bound, backtracking in the probe set;

selecting a respective configuration of helper variables at random based on a probability proportional to a difference between the energy gap and the lower bound;

solving a second linear program to determine a first new lower bound;

in response to the first new lower bound exceeding the lower bound, setting the lower bound equal to the first new lower bound;

performing a local search to determine a second new lower bound; and

in response to the second new lower bound exceeding the lower bound, setting the lower bound equal to the second new lower bound.

2 . The method of claim 1 , further comprising:

repeating the iterating, selecting, determining, backtracking, selecting, solving, setting and performing until the end condition of an earliest of: the lower bound exceeds a determined threshold, a defined time has elapsed, or a defined number of cycles has been performed.

3 . A system to solve problems, the system comprising:

at least one processor; and

at least one nontransitory processor-readable medium communicatively coupled to the at least one processor and which stores at least one of processor-executable instructions or data, which when executed by the at least one processor causes the at least one processor to:

initialize a probe set;

initialize a lower bound;

for a number of cycles until an end condition is reached:

iterate over an expansion of the probe set and a configuration of helper variables to solve a first linear program for a quadratic unconstrained binary optimization (QUBO) problem and an energy gap which corresponds to the QUBO problem;

select an expanded probe set with a sufficiently small number of solutions for which the energy gap exceeds the lower bound;

determine whether there are no solutions for which the energy gap exceeds the lower bound,

in response to a determination that there are no solutions for which the energy gap exceeds the lower bound, backtrack in the probe set;

select a respective configuration of helper variables at random based on a probability proportional to a difference between the energy gap and the lower bound;

solve a second linear program to determine a first new lower bound;

in response to the first new lower bound exceeding the lower bond, set the lower bound equal to the first new lower bound;

perform a local search to determine a second new lower bound; and

in response to the second new lower bound exceeding the lower bound, set the lower bound equal to the second new lower bound.

4 . The system of claim 1 wherein the at least one processor repeats the cycles until end condition of an earliest of: the lower bound exceeds a determined threshold, a defined time has elapsed, or a defined number of cycles has been performed.

5 . A method of solving problems using one or more processors, the method as described and shown in the specification and drawings.

6 . A system to solve problems, the system as described and shown in the specification and drawings.