# Foundations for learning from noisy quantum experiments

arXiv: https://arxiv.org/abs/2204.13691 · HTML: https://mlsanity.com/paper/2204.13691/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 68 references that are in the map.
- First posted on arXiv 28 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [A Hierarchy for Replica Quantum Advantage](https://mlsanity.com/paper/2111.05874/) (2021)
- [Optimal learning of quantum Hamiltonians from high-temperature Gibbs states](https://mlsanity.com/paper/2108.04842/) (2021)

## Built on by (most cited first, 12 of 12)

- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Learning many-body Hamiltonians with Heisenberg-limited scaling](https://mlsanity.com/paper/2210.03030/) (2022)
- [Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix](https://mlsanity.com/paper/2212.04471/) (2022)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [The Complexity of NISQ](https://mlsanity.com/paper/2210.07234/) (2022)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Learning k-body Hamiltonians via compressed sensing](https://mlsanity.com/paper/2410.18928/) (2024)
- [Tight bounds on Pauli channel learning without entanglement](https://mlsanity.com/paper/2309.13461/) (2023)
- [What can we learn from quantum convolutional neural networks?](https://mlsanity.com/paper/2308.16664/) (2023)
- [Learning Quantum Processes with Quantum Statistical Queries](https://mlsanity.com/paper/2310.02075/) (2023)
- [Provable learning of quantum states with graphical models](https://mlsanity.com/paper/2309.09235/) (2023)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state preparation, dynamics, and measurement) are a priori unknown. We prove that, without any prior knowledge, if one can explore the full quantum state space by composing the operations, then every operation can be learned. When one cannot explore the full state space but all operations are approximately known and noise in Clifford gates is gate-independent, we find an efficient algorithm for learning all operations up to a single unlearnable parameter characterizing the fidelity of the initial state. For learning a noise channel on Clifford gates to a fixed accuracy, our algorithm uses quadratically fewer experiments than previously known protocols. Under more general conditions, the true description of the noise can be unlearnable; for example, we prove that no benchmarking protocol can learn gate-dependent Pauli noise on Clifford+T gates even under perfect state preparation and measurement. Despite not being able to learn the noise, we show that a noisy quantum computer that performs entangled measurements on multiple copies of an unknown state can yield a large advantage in learning properties of the state compared to a noiseless device that measures individual copies and then processes the measurement data using a classical computer. Concretely, we prove that noisy quantum computers with two-qubit gate error rate ε can achieve a learning task using N copies of the state, while NOmega(1/ε) copies are required classically.