  We introduce a novel quantum computing heuristic for solving the irregular
strip packing problem, a significant challenge in optimizing material usage
across various industries. This problem involves arranging a set of irregular
polygonal pieces within a fixed-height, rectangular container to minimize
waste. Traditional methods heavily rely on manual optimization by specialists,
highlighting the complexity and computational difficulty of achieving
quasi-optimal layouts. The proposed algorithm employs a quantum-inspired
heuristic that decomposes the strip packing problem into two sub-problems:
ordering pieces via the traveling salesman problem and spatially arranging them
in a rectangle packing problem. This strategy facilitates a novel application
of quantum computing to industrial optimization, aiming to minimize waste and
enhance material efficiency. Experimental evaluations using both classical and
quantum computational methods demonstrate the algorithm's efficacy. We evaluate
the algorithm's performance using the quantum approximate optimization
algorithm and the quantum alternating operator ansatz, through simulations and
real quantum computers, and compare it to classical approaches.
