CNOT-Distance, deciding whether a given invertible binary matrix can be implemented with at most K CNOT gates under all-to-all connectivity, is NP-complete.
Thus ex- act CNOT-count minimisation remains computation- ally hard even after routing constraints and restricted gate availability are removed
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CNOT-Distance is NP-complete under all-to-all connectivity
CNOT-Distance, deciding whether a given invertible binary matrix can be implemented with at most K CNOT gates under all-to-all connectivity, is NP-complete.