Benchmarking Quantum Computational Advantages on Supercomputers

The achievement of quantum computational advantage, also known as quantum supremacy, is a major milestone at which a quantum computer can solve a problem significantly faster than the world's most powerful classical computers. Two tasks, boson sampling and random quantum circuit sampling, have experimentally exhibited quantum advantages on photonic and superconducting platforms respectively. Classical benchmarking is essential, yet challenging, because these tasks are intractable for classical computers. This study reviews models, algorithms and large-scale simulations of these two sampling tasks. These approaches continue to hold substantial significance for research in both current noisy intermediate-scale quantum (NISQ) systems and future fault-tolerant quantum computing.