Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively ‘undone’ for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.

量子错误缓解已被提出作为一种手段，用于消除近期量子计算中不需要的和不可避免的错误，而不会产生容错方案所需的沉重资源开销。最近，错误缓解功能已成功应用于减少近期应用中的噪声。然而，在这项工作中，我们确定了对于更大系统尺寸可以有效“消除”量子噪声的程度的强烈限制。我们的框架严格捕获了当今使用的大型错误缓解方案。通过将误差缓解与统计推理问题联系起来，我们表明，即使在与当前实验相当的浅电路深度下，在最坏的情况下也需要超多项式数量的样本来估计无噪声可观察对象的期望值，这是误差缓解的主要任务。值得注意的是，我们的结构意味着噪声引起的加扰可以在比以前认为的要小得多的深度开始。噪声还通过限制量子机器学习中的核估计来影响其他近期应用，导致变分量子算法中更早地出现噪声诱导的贫瘠平台，并排除了在存在噪声的情况下估计期望值或准备哈密顿量基态时的指数量子加速。