Google’s quantum supremacy experiment heralded a transition point where quantum computers can evaluate a computational task, random circuit sampling, faster than classical supercomputers. We examine the constraints on the region of quantum advantage for quantum circuits with a larger number of qubits and gates than experimentally implemented. At near-term gate fidelities, we demonstrate that quantum supremacy is limited to circuits with a qubit count and circuit depth of a few hundred. Larger circuits encounter two distinct boundaries: a return of a classical advantage and practically infeasible quantum runtimes. Decreasing error rates cause the region of a quantum advantage to grow rapidly. At error rates required for early implementations of the surface code, the largest circuit size within the quantum supremacy regime coincides approximately with the smallest circuit size needed to implement error correction. Thus, the boundaries of quantum supremacy may fortuitously coincide with the advent of scalable, error-corrected quantum computing.

谷歌的量子霸权实验预示着一个转折点，在这个转折点上，量子计算机可以比传统超级计算机更快地评估计算任务、随机电路采样。我们检查了具有比实验实现更多数量的量子位和门的量子电路的量子优势区域的限制。在近期门保真度方面，我们证明量子霸权仅限于量子位计数和电路深度为几百的电路。更大的电路遇到两个截然不同的边界：经典优势的回归和实际上不可行的量子运行时间。降低错误率会导致量子优势区域迅速扩大。以早期实现表面代码所需的错误率，量子霸权体制内的最大电路尺寸与实现纠错所需的最小电路尺寸大致一致。因此，量子霸权的边界可能偶然与可扩展的、纠错的量子计算的出现相吻合。