In this paper, we study the problem of digital pre/post-coding design in multiple-input multiple-output (MIMO) systems with 1-bit resolution per complex dimension. The optimal solution that maximizes the received signal-to-noise ratio relies on an NP-hard combinatorial problem that requires exhaustive searching with exponential complexity. By using the principles of alternating optimization and quantum annealing (QA), an iterative QA-based algorithm is proposed that achieves near-optimal performance with polynomial complexity. The algorithm is associated with a rigorous mathematical framework that casts the pre/post-coding vector design to appropriate real-valued quadratic unconstrained binary optimization (QUBO) problems. Experimental results in a state-of-the-art D-WAVE QA device validate the efficiency of the proposed algorithm. To further improve the efficiency of the D-WAVE quantum device, a new pre-processing technique which preserves the quadratic QUBO matrix from the detrimental effects of the Hamiltonian noise through non-linear companding, is proposed. The proposed pre-processing technique significantly improves the quality of the D-WAVE solutions as well as the occurrence probability of the optimal solution.

翻译：本文研究了每复维度1比特分辨率的多输入多输出（MIMO）系统中数字预/后编码的设计问题。最大化接收信噪比的最优解依赖于一个NP难组合问题，该问题需要指数复杂度的穷举搜索。利用交替优化和量子退火（QA）原理，本文提出了一种基于QA的迭代算法，该算法以多项式复杂度实现了接近最优的性能。该算法与一个严格的数学框架相关联，该框架将预/后编码向量设计转化为适当的实值二次无约束二进制优化（QUBO）问题。在先进的D-WAVE QA设备上的实验结果验证了所提算法的有效性。为了进一步提高D-WAVE量子设备的效率，本文提出了一种新的预处理技术，该技术通过非线性压扩保护二次QUBO矩阵免受哈密顿量噪声的有害影响。所提出的预处理技术显著提高了D-WAVE解的质量以及最优解的出现概率。