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：在本文中,我们提出一种新的方法,将NP-硬无线频道分配问题作为更高顺序的不受限制的二进制优化(HUBO)来提出,格罗佛适应性搜索(GAS)用来为解决问题提供二次加速。常规方法依赖于频道指数的一热编码,从而形成二次配方。相反,我们设想频道指数的上升和下降二进制编码,构建一个特定的量子电路,并得出GAS要求的qubits和门的确切数量。我们的分析澄清,拟议的HUBO配方与传统的四进制相比,大大减少了qubits的数量和询问的复杂性。这一优势的实现是以数量增加的量子门为代价的,我们通过拟议的递增二进二进制编码可以减少这些数量。