Constant Runtime Error Mitigation via Restricted Evolution

Error mitigation techniques, while instrumental in extending the capabilities of near-term quantum computers, often suffer from exponential resource scaling with noise levels. To address this limitation, we introduce a novel approach, namely, constant runtime error mitigation by restricted evolution (EMRE). Through numerical simulations, we demonstrate that EMRE surpasses the performance of Probabilistic Error Cancellation (PEC) while maintaining constant sampling overhead. The constant sampling overhead comes at the cost of a small non-zero bias. We provide a methodology to compute the optimal bias by connecting it to a resource-theoretic measure. We also evaluate bounds on the bias under different noise models and give exact results for the case of depolarizing and dephasing noise. Using these exact results, we derive an even more efficient strategy to implement EMRE. Additionally, we introduce Hybrid EMREs (HEMREs), a continuous family of error mitigation protocols that encompass PEC and EMRE as special cases. HEMREs offer a tunable bias parameter, enabling a trade-off between sample complexity and error reduction. The numerical evidence suggests the scalability and practicality of our proposal. Hence, our error mitigation protocols provide flexibility in balancing error mitigation with computational overhead, catering to practical application requirements of near-term and early-fault tolerant quantum devices.