Optimal resource cost for error mitigation

One of the central problems for near-term quantum devices is to understand their ultimate potential and limitations. We address this problem in terms error mitigation by introducing a framework taking into account full expressibility devices, which optimal resource cost probabilistic cancellation method can be formalized. provide general methodology evaluating connecting it resource-theoretic quantifier defined with respect noisy operations that implement. employ our methods estimate mitigating class noise, where we obtain an achievable has generic advantage over previous evaluations, as well fundamental lower bound applicable broad implementable operations. improve bounds several noise models, give exact costs depolarizing dephasing precisely characterizing overhead while offering operational meaning measure mitigation. Our result particularly implies heuristic approach presented Temme et al. [K. Temme, S. Bravyi, J. M. Gambetta, Phys. Rev. Lett. 119, 180509 (2017)] even extended framework, putting limitations on provided extra degrees freedom inherent model.