Recent successes in producing intermediate-scale quantum devices have focused interest on establishing whether near-term devices could outperform classical computers for practical applications. A central question is whether noise can be overcome in the absence of quantum error correction or if it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical and quantum algorithms running on noisy devices for a large family of tasks that includes optimization and variational eigenstate solving. Our approach is based on entropic inequalities that determine how fast the quantum state converges to the fixed point of the noise model, together with established classical methods of Gibbs state simulation. Our techniques are extremely versatile and so may be applied to a large variety of algorithms, noise models and quantum computing architectures. We use our result to provide estimates for problems within reach of current experiments, such as quantum annealers or variational quantum algorithms. The bounds we obtain indicate that substantial quantum advantages are unlikely for classical optimization unless noise rates are decreased by orders of magnitude or the topology of the problem matches that of the device. This is the case even if the number of available qubits increases substantially.

最近在生产中等规模量子设备方面取得的成功将人们的兴趣集中在确定近期设备是否可以在实际应用中优于经典计算机。一个中心问题是在没有量子纠错的情况下是否可以克服噪声，或者它是否从根本上限制了任何潜在的量子优势。我们提出了一种透明的方式来比较在嘈杂设备上运行的经典算法和量子算法，以解决包括优化和变分本征态求解在内的一大类任务。我们的方法基于确定量子态收敛到噪声模型固定点的速度的熵不等式，以及已建立的经典吉布斯状态模拟方法。我们的技术非常通用，因此可以应用于多种算法，噪声模型和量子计算架构。我们使用我们的结果来估计当前实验范围内的问题，例如量子退火器或变分量子算法。我们获得的界限表明，除非噪声率降低几个数量级或问题的拓扑与设备的拓扑匹配，否则经典优化不太可能具有实质性的量子优势。即使可用量子比特的数量大幅增加，情况也是如此。我们获得的界限表明，除非噪声率降低几个数量级或问题的拓扑与设备的拓扑匹配，否则经典优化不太可能具有实质性的量子优势。即使可用量子比特的数量大幅增加，情况也是如此。我们获得的界限表明，除非噪声率降低几个数量级或问题的拓扑与设备的拓扑匹配，否则经典优化不太可能具有实质性的量子优势。即使可用量子比特的数量大幅增加，情况也是如此。