mlsanityData to 7 Oct 2026

Learning to predict arbitrary quantum processes

arXiv 2210.14894 ↗First posted 26 Oct 2022quant-ph cs.DS cs.ITcited by 34

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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.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). Builds on 27 of its 85 references that are in the map. First posted on arXiv 26 Oct 2022.

Builds on

27 of 85 references.

References · 27

  1. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  2. 2020Variational Quantum Algorithmscited by 687
  3. 2018Supervised learning with quantum enhanced feature spacescited by 654
  4. 2018Barren plateaus in quantum neural network training landscapescited by 624
  5. 2020Power of data in quantum machine learningcited by 336
  6. 2016Quantum Machine Learningcited by 325
  7. 2020Predicting Many Properties of a Quantum System from Very Few Measurementscited by 229
  8. 2021Generalization in quantum machine learning from few training datacited by 214
  9. 2021Quantum advantage in learning from experimentscited by 186
  10. 2021Information-theoretic bounds on quantum advantage in machine learningcited by 95
  11. 2021Provably efficient machine learning for quantum many-body problemscited by 91
  12. 2019Deep autoregressive models for the efficient variational simulation of many-body quantum systemscited by 64
15 more
  1. 2021Exponential separations between learning with and without quantum memorycited by 50
  2. 2022Out-of-distribution generalization for learning quantum dynamicscited by 49
  3. 2017Active learning machine learns to create new quantum experimentscited by 41
  4. 2022Classical surrogates for quantum learning modelscited by 39
  5. 2018Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problemcited by 16
  6. 2020Learning models of quantum systems from experimentscited by 16
  7. 2022Dynamical simulation via quantum machine learning with provable generalizationcited by 15
  8. 2020Classical Shadows With Noisecited by 13
  9. 2022Foundations for learning from noisy quantum experimentscited by 11
  10. 2021Learning low-degree functions from a logarithmic number of random queriescited by 8
  11. 2021Hamiltonian-Driven Shadow Tomography of Quantum Statescited by 4
  12. 2022Fermionic tomography and learningcited by 3
  13. 2015Beating the random assignment on constraint satisfaction problems of bounded degreecited by 2
  14. 2021Improved approximation algorithms for bounded-degree local Hamiltonianscited by 2
  15. 2020Beating Random Assignment for Approximating Quantum 2-Local Hamiltonian Problemscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 13; 2024: 12; 2025: 7; 2026: 1.

34 papers.

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  1. 2023Does provable absence of barren plateaus imply classical simulability?cited by 78
  2. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 33
  3. 2023A survey on the complexity of learning quantum statescited by 31
  4. 2022Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrixcited by 22
  5. 2023Improved machine learning algorithm for predicting ground state propertiescited by 22
  6. 2024Learning shallow quantum circuitscited by 20
  7. 2023The power and limitations of learning quantum dynamics incoherentlycited by 12
  8. 2025Artificial intelligence for representing and characterizing quantum systemscited by 9
  9. 2025Generative quantum advantage for classical and quantum problemscited by 9
  10. 2024Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equationscited by 7
  11. 2024Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuitscited by 7
  12. 2023Classical Verification of Quantum Learningcited by 6
22 more
  1. 2023Transition Role of Entangled Data in Quantum Machine Learningcited by 5
  2. 2023Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamicscited by 5
  3. 2023Learning unitaries with quantum statistical queriescited by 5
  4. 2024Online learning of a panoply of quantum objectscited by 5
  5. 2023Learning Quantum Processes with Quantum Statistical Queriescited by 4
  6. 2023Advantage of Quantum Machine Learning from General Computational Advantagescited by 4
  7. 2024Learning the structure of any Hamiltonian from minimal assumptionscited by 4
  8. 2023Post-variational quantum neural networkscited by 3
  9. 2024Concept learning of parameterized quantum models from limited measurementscited by 3
  10. 2025Role of scrambling and noise in temporal information processing with quantum systemscited by 3
  11. 2023Sample-efficient Model-based Reinforcement Learning for Quantum Controlcited by 2
  12. 2024Simple algorithms to test and learn local Hamiltonianscited by 2
  13. 2024Learning low-degree quantum objectscited by 2
  14. 2024Predicting quantum channels over general product distributionscited by 2
  15. 2025Physically Plausible Multi-System Trajectory Generation and Symmetry Discoverycited by 2
  16. 2024Testing classical properties from quantum datacited by 1
  17. 2025ResQ: A Novel Framework to Implement Residual Neural Networks on Analog Rydberg Atom Quantum Computerscited by 1
  18. 2023Efficient information recovery from Pauli noise via classical shadowcited by 0
  19. 2024Noise-tolerant learnability of shallow quantum circuits from statistics and the cost of quantum pseudorandomnesscited by 0
  20. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  21. 2025A Study on Stabilizer R'enyi Entropy Estimation using Machine Learningcited by 0
  22. 2026A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectracited by 0