Quantum information processing has the potential to substantially enhance how we learn from physical experiments, but coupling a quantum processor to an experimental sample introduces noise that can exponentially degrade learning even when the processor itself is fault-tolerant. In this work, we show that fault tolerance can nevertheless be leveraged to recover exponential speedups by embedding the unknown system into an arbitrarily high-distance quantum code with only constant error overhead and running a fault-tolerant learning algorithm. Using this $\textit{quantum uploading}$ procedure, we prove that both classical shadow tomography and the estimation of cubic observables can be performed exponentially faster than by any adaptive strategy that does not immediately upload the state into encoded memory. These separations hold even when the uploading stage is substantially noisier than the bare experimental interface. To prove them, we introduce the Heisenberg learning tree method, a flexible tool for obtaining learning lower bounds when the limited resource is not quantum replicas but an experimentally motivated constraint such as noise. We numerically illustrate the speedups in an astronomical imaging application, where quantum processing of individual uploaded photons locates an exoplanet obscured by a bright star using orders of magnitude fewer shots than unencoded baselines. Our results establish fault-tolerant quantum computation as a valuable tool for learning from quantum experiments.

翻译：量子信息处理有望显著提升我们从物理实验中学习的能力，但将量子处理器与实验样本耦合会引入噪声，即使处理器本身具有容错性，这种噪声也可能使学习能力呈指数级下降。在本研究中，我们证明，通过将未知系统嵌入任意高距离量子码（仅需恒定误差开销）并运行容错学习算法，仍可借助容错机制恢复指数级加速。利用这一"量子上传"过程，我们证明：相较于任何不立即将量子态上传至编码存储器的自适应策略，经典阴影层析成像以及三阶观测量的估计均可实现指数级加速。即使上传阶段的噪声远高于裸实验接口，这种性能差异依然成立。为证明这些结论，我们引入了海森堡学习树方法——一种灵活的工具，用于在有限资源非量子副本、而是噪声等实验约束条件下推导学习下界。我们在天文成像应用中数值验证了这种加速效果：通过对单个上传光子进行量子处理，以比非编码基线少数个数量级的拍摄次数，定位了被亮星遮蔽的系外行星。我们的研究结果确立了容错量子计算作为从量子实验中学习的有力工具。