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

文件GAP.h5、GRAPH_COLORING.h5与IP.h5包含了复现本文稿中展示的门分配(Gate Assignment)、图着色(Graph Coloring)以及整数规划(Integer Programming)问题相关配图所需的全部数据。
每个.h5格式文件均可通过Python库h5py打开。
每个对应单一问题类的.h5文件中，均包含以下键值：
• hubo_gate_requirements：一个结构化数组，包含RZ门(RZ)、RX门(RX)、CNOT门(CNOT)以及哈达玛(Hadamard)门的计数，以及HUBO问题建模中使用的量子比特(qubits)数量。通过主脚本，可将量子比特数直接映射至对应的问题规模。
• qubo_gate_requirements：与上述结构一致的结构化数组，但对应QUBO建模场景。
• hubo_nbr_qubits_<x>_depth_<y>：一个结构化数组，包含针对<x>个量子比特、<y>层量子近似优化算法(Quantum Approximate Optimization Algorithm, QAOA)的HUBO建模场景所执行的QAOA参数（β与γ）以及对应的近似比。针对主脚本中提及的每一组量子比特规模<x>与迭代深度<y>，均提供了对应的数据集。
• qubo_nbr_qubits_<x>_depth_<y>：对应QUBO建模场景的同类QAOA数据集。