Because noisy intermediate-scale quantum (NISQ) machines accumulate errors quickly, we need new approaches to designing NISQ-aware algorithms and assessing their performance. Algorithms with characteristics that appear less desirable under ideal circumstances, such as lower success probability, may in fact outperform their ideal counterparts on existing hardware. We propose an adaptation of Grover’s algorithm, subdividing the phase flip into segments to replace a digital counter and complex phase flip decision logic. We applied this approach to obtain the best solution of the MAX-CUT problem in sparse graphs, utilizing multicontrol, Toffoli-like gates with residual phase shifts. We implemented this algorithm on IBM Q processors and succeeded in solving a five-vertex MAX-CUT problem, demonstrating amplitude amplification on four qubits. This approach will be useful for a range of problems, and may shorten the time to reaching quantum advantage.

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