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This paper presents novel methods for optimizing multi-controlled quantum gates, which naturally arise in high-level quantum programming. Our primary approach involves rewriting U (2) gates as SU (2) gates, utilizing one auxiliary qubit for phase correction. This reduces the number of CNOT gates required to decompose any multi-controlled quantum gate from O (n²) to at most 32n. Additionally, we can reduce the number of CNOTs for multi-controlled Pauli gates from 16n to 12n and propose an optimization to reduce the number of controlled gates in high-level quantum programming. We have implemented these optimizations in the Ket quantum programming platform and demonstrated significant reductions in the number of gates. For instance, for a Grover's algorithm layer with 114 qubits, we achieved a reduction in the number of CNOTs from 101, 245 to 2, 684. This reduction in the number of gates significantly impacts the execution time of quantum algorithms, thereby enhancing the feasibility of executing them on NISQ computers.
Rosa et al. (Sat,) studied this question.