Exponential speedups in fault-tolerant processing of quantum experiments

TL;DR

This paper demonstrates that fault-tolerant quantum processing can achieve exponential speedups in learning from quantum experiments by embedding systems into high-distance codes and using quantum uploading, even under noisy conditions.

Contribution

It introduces the quantum uploading procedure and Heisenberg learning tree method, enabling exponential speedups in quantum learning tasks despite noise and limited resources.

Findings

Quantum uploading enables exponential speedups in shadow tomography and observable estimation.

Speedups are robust even when uploading is noisier than the experimental interface.

Numerical simulations show significant efficiency gains in astronomical imaging applications.

Abstract

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.