# The power and limitations of learning quantum dynamics incoherently

arXiv: https://arxiv.org/abs/2303.12834 · HTML: https://mlsanity.com/paper/2303.12834/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 22 Mar 2023.

## Builds on (most cited first, 15 of 15)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets](https://mlsanity.com/paper/2007.04900/) (2020)
- [Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix](https://mlsanity.com/paper/2212.04471/) (2022)
- [Learning models of quantum systems from experiments](https://mlsanity.com/paper/2002.06169/) (2020)
- [Dynamical simulation via quantum machine learning with provable generalization](https://mlsanity.com/paper/2204.10269/) (2022)
- [Long-time simulations with high fidelity on quantum hardware](https://mlsanity.com/paper/2102.04313/) (2021)
- [Scalably learning quantum many-body Hamiltonians from dynamical data](https://mlsanity.com/paper/2209.14328/) (2022)

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

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Certifying almost all quantum states with few single-qubit measurements](https://mlsanity.com/paper/2404.07281/) (2024)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [PennyCoder: Efficient Domain-Specific LLMs for PennyLane-Based Quantum Code Generation](https://mlsanity.com/paper/2507.19562/) (2025)
- [Transition Role of Entangled Data in Quantum Machine Learning](https://mlsanity.com/paper/2306.03481/) (2023)
- [Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics](https://mlsanity.com/paper/2308.14239/) (2023)
- [Exact gradients for linear optics with single photons](https://mlsanity.com/paper/2409.16369/) (2024)
- [Separable Power of Classical and Quantum Learning Protocols Through the Lens of No-Free-Lunch Theorem](https://mlsanity.com/paper/2405.07226/) (2024)

## Abstract (arXiv)

Quantum process learning is emerging as an important tool to study quantum systems. While studied extensively in coherent frameworks, where the target and model system can share quantum information, less attention has been paid to whether the dynamics of quantum systems can be learned without the system and target directly interacting. Such incoherent frameworks are practically appealing since they open up methods of transpiling quantum processes between the different physical platforms without the need for technically challenging hybrid entanglement schemes. Here we provide bounds on the sample complexity of learning unitary processes incoherently by analyzing the number of measurements that are required to emulate well-established coherent learning strategies. We prove that if arbitrary measurements are allowed, then any efficiently representable unitary can be efficiently learned within the incoherent framework; however, when restricted to shallow-depth measurements only low-entangling unitaries can be learned. We demonstrate our incoherent learning algorithm for low entangling unitaries by successfully learning a 16-qubit unitary on textttibmqkolkata, and further demonstrate the scalabilty of our proposed algorithm through extensive numerical experiments.