The pursuit of practical quantum utility on near-term quantum processors is critically challenged by their inherent noise. Quantum error mitigation (QEM) techniques are leading solutions to improve computation fidelity with relatively low qubit-overhead, while full-scale quantum error correction remains a distant goal. However, QEM techniques incur substantial measurement overheads, especially when applied to families of quantum circuits parameterized by classical inputs. Focusing on zero-noise extrapolation (ZNE), a widely adopted QEM technique, here we devise the surrogate-enabled ZNE (S-ZNE), which leverages classical learning surrogates to perform ZNE entirely on the classical side. Unlike conventional ZNE, whose measurement cost scales linearly with the number of circuits, S-ZNE requires only constant measurement overhead for an entire family of quantum circuits, offering superior scalability. Theoretical analysis indicates that S-ZNE achieves accuracy comparable to conventional ZNE in many practical scenarios, and numerical experiments on up to 100-qubit ground-state energy and quantum metrology tasks confirm its effectiveness. Our approach provides a template that can be effectively extended to other quantum error mitigation protocols, opening a promising path toward scalable error mitigation.

翻译：在近期量子处理器上实现实用量子优势的追求，因其固有噪声而面临严峻挑战。量子误差缓解（QEM）技术是当前以较低量子比特开销提升计算保真度的主流解决方案，而全规模的量子纠错仍是一个遥远目标。然而，QEM技术会带来显著的测量开销，尤其当应用于由经典输入参数化的量子电路族时。聚焦于广泛采用的量子误差缓解技术——零噪声外推（ZNE），本文设计了代理辅助的ZNE（S-ZNE），该方法利用经典学习代理在经典侧完全执行ZNE。与传统ZNE的测量成本随电路数量线性增长不同，S-ZNE对整个量子电路族仅需恒定的测量开销，具备更优的可扩展性。理论分析表明，在许多实际场景中，S-ZNE能达到与传统ZNE相当的精度；在多达100量子比特的基态能量和量子计量任务上的数值实验也验证了其有效性。我们的方法为有效扩展至其他量子误差缓解协议提供了模板，开辟了一条通向可扩展误差缓解的有前景的路径。