A proposed Grover-based maximum clique solver claims O(sqrt(2^n)) iterations and O(1) measurements by pre-encoding the clique size, but the pre-encoding itself costs exponentially many gates and is excluded from the headline complexity.
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Efficient Maximum Clique Detection via Grover's Algorithm with Real-time Global Size Tracking
A proposed Grover-based maximum clique solver claims O(sqrt(2^n)) iterations and O(1) measurements by pre-encoding the clique size, but the pre-encoding itself costs exponentially many gates and is excluded from the headline complexity.