Abstract

In recent years, quantum learning theory has been centered around the thesis that quantum information processing can enable experimental discoveries that would otherwise be impossible. Early results established worst-case exponential quantum speedups for estimating properties of quantum systems, but realizing these speedups in near-term experiments has remained a major challenge. In this talk, we begin by understanding why: even with fault-tolerant quantum computers, the noise incurred when learning from Nature degrades the very primitives that underlie quantum speedups. We develop a complexity-theoretic framework for quantum experiments in which fault-tolerant devices learn from Nature through noisy couplings, and prove exponential information-theoretic lower bounds on quantum-enhanced learning strategies in this model. The core message is that the ideal assumptions of quantum learning theory are misleading: noise can erase the most prominent canonical quantum speedups. With this more nuanced picture in hand, we then lay out directions toward realizing quantum speedups in realistic experimental settings and make concrete progress on them. We describe how noise instantiates a data-uploading bottleneck unique to quantum mechanics, forcing sophisticated learning procedures to incur severe errors when they must repeatedly act upon unencoded quantum data. However, by leveraging developments in fault-tolerant quantum computation, we show that arbitrary, unknown quantum data can be efficiently uploaded into an encoded quantum memory and processed fault tolerantly. By developing new techniques in quantum learning theory, we prove that this uploading procedure enables the recovery of exponential speedups that are otherwise degraded by the data-uploading bottleneck, enabling quantum learning primitives to operate on data from a wide array of quantum experiments.

Personal information

Ishaan is a first-year graduate student at the Harvard Quantum Initiative advised by Prof. Jordan Cotler. His interests lie in utilizing quantum information processing to power our scientific exploration of the natural world, spanning applications such as chemistry, high-energy physics, and astronomy. Recently, his work has centered on understanding how abstract theoretical insights from quantum sensing and learning theory can be realized as practically meaningful gains in future quantum-enhanced experiments. This includes designing quantum-enhanced experiments that retain quantum advantage in the presence of noise, proposing quantum sensing strategies that leverage near-term quantum devices, and developing learning algorithms for characterizing molecular systems with quantum probes.

Reference

https://arxiv.org/abs/2512.10929, arXiv:2602.17591