We present a subproblemation scheme for heuristical solving of the JSP (Job Reassignment Problem). The cost function of the JSP is described via a QUBO hamiltonian to allow implementation in both gate-based and annealing quantum computers. For a job pool of $K$ jobs, $\mathcal{ O}(K^2)$ binary variables -- qubits -- are needed to solve the full problem, for a runtime of $\mathcal{ O}(2^{ K^2})$. With the presented heuristics, the average variable number of each of the $D$ subproblems to solve is $\mathcal{ O}(K^2/2D)$, and the expected total runtime $\mathcal{ O}(D2^{ K^2/2D})$, achieving an exponential speedup.
Categories: quant-ph