# Learning to predict arbitrary quantum processes

arXiv: https://arxiv.org/abs/2210.14894 · HTML: https://mlsanity.com/paper/2210.14894/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 85 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 27 of 27)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [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)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [Classical surrogates for quantum learning models](https://mlsanity.com/paper/2206.11740/) (2022)
- [Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem](https://mlsanity.com/paper/1810.10938/) (2018)
- [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)
- [Classical Shadows With Noise](https://mlsanity.com/paper/2011.11580/) (2020)
- [Foundations for learning from noisy quantum experiments](https://mlsanity.com/paper/2204.13691/) (2022)
- [Learning low-degree functions from a logarithmic number of random queries](https://mlsanity.com/paper/2109.10162/) (2021)
- [Hamiltonian-Driven Shadow Tomography of Quantum States](https://mlsanity.com/paper/2102.10132/) (2021)
- [Fermionic tomography and learning](https://mlsanity.com/paper/2207.14787/) (2022)
- [Beating the random assignment on constraint satisfaction problems of bounded degree](https://mlsanity.com/paper/1505.03424/) (2015)
- [Improved approximation algorithms for bounded-degree local Hamiltonians](https://mlsanity.com/paper/2105.01193/) (2021)
- [Beating Random Assignment for Approximating Quantum 2-Local Hamiltonian Problems](https://mlsanity.com/paper/2012.12347/) (2020)

## Built on by (most cited first, 30 of 35)

- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [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)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [The power and limitations of learning quantum dynamics incoherently](https://mlsanity.com/paper/2303.12834/) (2023)
- [Generative quantum advantage for classical and quantum problems](https://mlsanity.com/paper/2509.09033/) (2025)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations](https://mlsanity.com/paper/2408.08639/) (2024)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Classical Verification of Quantum Learning](https://mlsanity.com/paper/2306.04843/) (2023)
- [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)
- [Learning unitaries with quantum statistical queries](https://mlsanity.com/paper/2310.02254/) (2023)
- [Online learning of a panoply of quantum objects](https://mlsanity.com/paper/2406.04245/) (2024)
- [Learning the structure of any Hamiltonian from minimal assumptions](https://mlsanity.com/paper/2410.21635/) (2024)
- [Learning Quantum Processes with Quantum Statistical Queries](https://mlsanity.com/paper/2310.02075/) (2023)
- [Advantage of Quantum Machine Learning from General Computational Advantages](https://mlsanity.com/paper/2312.03057/) (2023)
- [Post-variational quantum neural networks](https://mlsanity.com/paper/2307.10560/) (2023)
- [Concept learning of parameterized quantum models from limited measurements](https://mlsanity.com/paper/2408.05116/) (2024)
- [Role of scrambling and noise in temporal information processing with quantum systems](https://mlsanity.com/paper/2505.10080/) (2025)
- [Sample-efficient Model-based Reinforcement Learning for Quantum Control](https://mlsanity.com/paper/2304.09718/) (2023)
- [Simple algorithms to test and learn local Hamiltonians](https://mlsanity.com/paper/2404.06282/) (2024)
- [Learning low-degree quantum objects](https://mlsanity.com/paper/2405.10933/) (2024)
- [Predicting quantum channels over general product distributions](https://mlsanity.com/paper/2409.03684/) (2024)
- [Testing classical properties from quantum data](https://mlsanity.com/paper/2411.12730/) (2024)
- [Discovering Phase Space Structure in Learned Hamiltonian Systems](https://mlsanity.com/paper/2509.23003/) (2025)
- [ResQ: A Novel Framework to Implement Residual Neural Networks on Analog Rydberg Atom Quantum Computers](https://mlsanity.com/paper/2506.21537/) (2025)
- [Provable learning separation for predicting time-evolution of quantum many-body systems](https://mlsanity.com/paper/2607.06472/) (2026)

## Abstract (arXiv)

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process E over n qubits. For a wide range of distributions D on arbitrary n-qubit states, we show that this ML algorithm can learn to predict any local property of the output from the unknown process~E, with a small average error over input states drawn from D. The ML algorithm is computationally efficient even when the unknown process is a quantum circuit with exponentially many gates. Our algorithm combines efficient procedures for learning properties of an unknown state and for learning a low-degree approximation to an unknown observable. The analysis hinges on proving new norm inequalities, including a quantum analogue of the classical Bohnenblust-Hille inequality, which we derive by giving an improved algorithm for optimizing local Hamiltonians. Numerical experiments on predicting quantum dynamics with evolution time up to 106 and system size up to 50 qubits corroborate our proof. Overall, our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.