Supporting Information for Resource-Efficient Quantum Optimization via Higher-Order Encoding

The files GAP.h5, GRAPH_COLORING.h5, and IP.h5 contain all data required to reproduce the figures for the Gate Assignment, Graph Coloring, and Integer Programming problems presented in the manuscript.

Each .h5 file can be opened using the Python package h5py.

Within each .h5 file (one per problem class), the following keys are provided:

• hubo_gate_requirements: A structured array containing the counts of RZ, RX, CNOT, and Hadamard gates, as well as the number of qubits used in the HUBO problem formulation. Using the main script, the number of qubits can be directly mapped to the corresponding problem size.

• qubo_gate_requirements: The same structured array as above, but for the QUBO formulation.

• hubo_nbr_qubits_<x>_depth_<y>: A structured array containing the QAOA parameters (beta and gamma) and the corresponding approximation ratios for QAOA executed on the HUBO formulation with <x> qubits and <y> QAOA layers. For each qubit size <x> and depth <y> described in the main script, a corresponding dataset is provided.

• qubo_nbr_qubits_<x>_depth_<y>: The analogous QAOA data for the QUBO formulation