mlsanityData to 7 Oct 2026

Dynamical simulation via quantum machine learning with provable generalization

arXiv 2204.10269 ↗First posted 21 Apr 2022quant-ph cs.LGcited by 15

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Abstract (arXiv)

Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. This provides a guarantee that our algorithm is resource-efficient, both in terms of qubit and data requirements. Our numerics exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 19 of its 52 references that are in the map. First posted on arXiv 21 Apr 2022.

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19 of 52 references.

References · 19

  1. 2020Variational Quantum Algorithmscited by 687
  2. 2018Barren plateaus in quantum neural network training landscapescited by 624
  3. 2020The power of quantum neural networkscited by 377
  4. 2021Generalization in quantum machine learning from few training datacited by 214
  5. 2021Supervised quantum machine learning models are kernel methodscited by 199
  6. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
  7. 2020Absence of Barren Plateaus in Quantum Convolutional Neural Networkscited by 124
  8. 2020Entanglement Induced Barren Plateauscited by 101
  9. 2021Encoding-dependent generalization bounds for parametrized quantum circuitscited by 81
  10. 2020Effect of barren plateaus on gradient-free optimizationcited by 79
  11. 2020On barren plateaus and cost function locality in variational quantum algorithmscited by 36
  12. 2020Pseudo-dimension of quantum circuitscited by 30
7 more
  1. 2020Reformulation of the No-Free-Lunch Theorem for Entangled Data Setscited by 28
  2. 2021On the statistical complexity of quantum circuitscited by 25
  3. 2021Structural risk minimization for quantum linear classifierscited by 24
  4. 2021Sample Complexity of Learning Parametric Quantum Circuitscited by 15
  5. 2021Long-time simulations with high fidelity on quantum hardwarecited by 8
  6. 2021Quantum constraint learning for quantum approximate optimization algorithmcited by 3
  7. 2022A quantum generative model for multi-dimensional time series using Hamiltonian learningcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 6; 2024: 5; 2025: 2; 2026: 1.

15 papers.

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  1. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  2. 2022Learning to predict arbitrary quantum processescited by 34
  3. 2023A survey on the complexity of learning quantum statescited by 31
  4. 2024Learning shallow quantum circuitscited by 20
  5. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  6. 2024Variational quantum simulation: a case study for understanding warm startscited by 14
  7. 2023The power and limitations of learning quantum dynamics incoherentlycited by 12
  8. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  9. 2025A Primer on Quantum Machine Learningcited by 9
  10. 2024Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuitscited by 7
  11. 2024Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Surveycited by 7
  12. 2023Transition Role of Entangled Data in Quantum Machine Learningcited by 5
3 more
  1. 2024Predicting quantum channels over general product distributionscited by 2
  2. 2025Fragmentation is Efficiently Learnable by Quantum Neural Networkscited by 0
  3. 2026Multitask Learning for Earth Observation Data Classification with Hybrid Quantum Networkcited by 0