 |
Center for Nonlinear Studies |
One of the central problems for near-term quantum devices is to understand their ultimate potential and limitations. We address this problem in terms of quantum error mitigation in two approaches. We first investigate the ultimate performance of one of the prominent error-mitigation protocols known as probabilistic error cancellation. To this end, we introduce a framework that takes into account the full expressibility of near-term devices, in which the optimal resource cost required for probabilistic error cancellation can be formalized. We provide a general methodology for evaluating the optimal cost by connecting it to a resource-theoretic quantifier defined with respect to the noisy operations that devices can implement. We apply our methods to a general class of noise and obtain an achievable cost that has a generic advantage over previous evaluations, as well as a fundamental lower bound applicable to a broad class of noisy implementable operations.
We then extend our investigation beyond probabilistic error cancellation and ask: What are the ultimate performance limits universally imposed on all possible error-mitigation strategies? Here, we derive a fundamental bound on the sampling overhead that applies to a general class of error-mitigation protocols, assuming only the laws of quantum mechanics. We use it to show that (1) the sampling overhead to mitigate local depolarizing noise for layered circuits must scale exponentially with circuit depth, and (2) the optimality of probabilistic error cancellation method among all strategies in mitigating a certain class of noise.
Host: LANL Quantum Initiative and CNLS