Resource efficient transfer learning approach for error mitigation of quantum circuits at scale

Large-scale fault-tolerant quantum computers are likely to enable new solutions for problems known to be hard for classical computers. This potential is tempered by the reality that hardware is exceptionally fragile and error-prone, forming a bottleneck in the development of novel applications. While error suppression techniques can dramatically boost algorithmic performance, inherent and irreversible errors, such as T1 processes, limit the ability of achieving quantum utility at scale. Error mitigation techniques provide a route to go beyond that limit at the price of additional resources overhead. Some of these approaches, such as probabilistic error cancellation (PEC), aim to collect a full description of the noise model to facilitate noise suppression. However, this requires over-sampling, which is costly to acquire and scales poorly as the number of qubits increases. In this work, we develop a new, scalable error mitigation approach based on training machine learning models on real device data. We focus on problems where the quantity of interest is a set of expectation values, such as quantum simulations or variational quantum eigensolvers (VQE). Using non-parametric ensemble models, we machine-learn the approximate inverse noise map for a subset of quantum observables. This is achieved by training models on a closely-related family of circuits which are efficiently simulable, and then using transfer learning to apply the learned inverse noise map to the circuits of interest. As a demonstration of our approach, we estimate Pauli observables and show a consistent ability to mitigate errors with a significantly reduced runtime compared to established mitigation techniques such as PEC and zero-noise extrapolation (ZNE).