In this paper, we propose a novel method of formulating an NP-hard wireless channel assignment problem as a higher-order unconstrained binary optimization (HUBO), where the Grover adaptive search (GAS) is used to provide a quadratic speedup for solving the problem. The conventional method relies on a one-hot encoding of the channel indices, resulting in a quadratic formulation. By contrast, we conceive ascending and descending binary encodings of the channel indices, construct a specific quantum circuit, and derive the exact numbers of qubits and gates required by GAS. Our analysis clarifies that the proposed HUBO formulation significantly reduces the number of qubits and the query complexity compared with the conventional quadratic formulation. This advantage is achieved at the cost of an increased number of quantum gates, which we demonstrate can be reduced by our proposed descending binary encoding.

翻译：本文提出一种将NP难无线信道分配问题表述为高阶无约束二进制优化（HUBO）的新方法，并采用Grover自适应搜索（GAS）为求解该问题提供二次加速。传统方法依赖信道索引的独热编码，导致问题呈二次型表述；相比之下，我们设计了信道索引的升序与降序二进制编码，构建了特定量子电路，并推导出GAS所需的精确量子比特数与量子门数量。分析表明，与传统二次型表述相比，所提出的HUBO表述显著降低了量子比特数量与查询复杂度。这一优势以量子门数量增加为代价，我们通过提出的降序二进制编码可有效减少这些门数量。