Explore Simpler Eigenmarking: Quantum Entailment Model Checking
This work addresses the challenges of implementing Grover search for implication-based model checking, particularly the requirement of minority-state conditions and the difficulty of executing highly entangling operations on near-term quantum hardware. To overcome these limitations, the authors propose a simplified Eigenmarking scheme that employs only a single ancillary qubit and a universal two-qubit controlled-phase gate (CCZ), reducing the original multi-controlled phase rotation to a doubly controlled operation. This approach substantially diminishes reliance on high-entanglement states while preserving effective amplitude amplification and unsatisfiability detection capabilities. Consequently, it significantly alleviates hardware demands and enhances scalability. Simulation results demonstrate that the proposed method achieves markedly superior performance, with a minimum relative local winning rate of W = 3.17 and discriminability of D = 0.769, outperforming both conventional marking (W = 0.67, D = 0.19) and fine-grained marking (W = 0.28, D = 0.55).