Applying quantum annealing or current quantum-/physics-inspired algorithms for MIMO detection always abandon the direct gray-coded bit-to-symbol mapping in order to obtain Ising form, leading to inconsistency errors. This often results in slow convergence rates and error floor, particularly with high-order modulations. We propose HOPbit, a novel MIMO detector designed to address this issue by transforming the MIMO detection problem into a higher-order unconstrained binary optimization (HUBO) problem while maintaining gray-coded bit-to-symbol mapping. The method then employs the simulated probabilistic bits (p-bits) algorithm to directly solve HUBO without degradation. This innovative strategy enables HOPbit to achieve rapid convergence and attain near-optimal maximum-likelihood performance in most scenarios, even those involving high-order modulations. The experiments show that HOPbit surpasses ParaMax by several orders of magnitude in terms of bit error rate (BER) in the context of 12-user massive and large MIMO systems even with computing resources. In addition, HOPbit achieves lower BER rates compared to other traditional detectors.
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