mlsanityData to 7 Oct 2026

Predicting Many Properties of a Quantum System from Very Few Measurements

arXiv 2002.08953 ↗First posted 18 Feb 2020quant-ph cs.IT cs.LGcited by 229

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Abstract (arXiv)

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log M measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

Key facts. Cited by 229 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Feb 2020.

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Citing papers per year: 2021: 26; 2022: 37; 2023: 44; 2024: 47; 2025: 39; 2026: 36.

229 papers.

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  1. 2021Quantum advantage in learning from experimentscited by 186
  2. 2021Information-theoretic bounds on quantum advantage in machine learningcited by 95
  3. 2021Provably efficient machine learning for quantum many-body problemscited by 91
  4. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
  5. 2023Does provable absence of barren plateaus imply classical simulability?cited by 78
  6. 2021Training Quantum Embedding Kernels on Near-Term Quantum Computerscited by 69
  7. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  8. 2021Exponential separations between learning with and without quantum memorycited by 50
  9. 2022Out-of-distribution generalization for learning quantum dynamicscited by 49
  10. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 48
  11. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40
  12. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
38 more
  1. 2022Learning to predict arbitrary quantum processescited by 34
  2. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 33
  3. 2023Towards provably efficient quantum algorithms for large-scale machine-learning modelscited by 32
  4. 2023On quantum backpropagation, information reuse, and cheating measurement collapsecited by 32
  5. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
  6. 2023A survey on the complexity of learning quantum statescited by 31
  7. 2023Shadows of quantum machine learningcited by 31
  8. 2021Quantum machine learning of large datasets using randomized measurementscited by 30
  9. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 24
  10. 2022Learning many-body Hamiltonians with Heisenberg-limited scalingcited by 22
  11. 2022Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrixcited by 22
  12. 2023Improved machine learning algorithm for predicting ground state propertiescited by 22
  13. 2022Quantum Policy Gradient Algorithm with Optimized Action Decodingcited by 21
  14. 2023Quantum anomaly detection in the latent space of proton collision events at the LHCcited by 21
  15. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  16. 2023Learning quantum Hamiltonians at any temperature in polynomial timecited by 20
  17. 2024Learning shallow quantum circuitscited by 20
  18. 2023On the Sample Complexity of Quantum Boltzmann Machine Learningcited by 18
  19. 2023On fundamental aspects of quantum extreme learning machinescited by 18
  20. 2021Near-Optimal Quantum Algorithms for Multivariate Mean Estimationcited by 16
  21. 2022Flexible learning of quantum states with generative query neural networkscited by 16
  22. 2021A semi-agnostic ansatz with variable structure for quantum machine learningcited by 15
  23. 2022Non-IID Quantum Federated Learning with One-shot Communication Complexitycited by 15
  24. 2023Learning quantum states and unitaries of bounded gate complexitycited by 15
  25. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  26. 2021Machine learning discovery of new phases in programmable quantum simulator snapshotscited by 13
  27. 2022The Complexity of NISQcited by 13
  28. 2022QuEst: Graph Transformer for Quantum Circuit Reliability Estimationcited by 13
  29. 2022Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulationcited by 13
  30. 2022Quantum Local Differential Privacy and Quantum Statistical Query Modelcited by 12
  31. 2022Adaptive Online Learning of Quantum Statescited by 12
  32. 2023The power and limitations of learning quantum dynamics incoherentlycited by 12
  33. 2023A Unified Framework for Trace-induced Quantum Kernelscited by 12
  34. 2024'Eliv'agar: Efficient Quantum Circuit Search for Classificationcited by 12
  35. 2022Tight Bounds for Quantum State Certification with Incoherent Measurementscited by 11
  36. 2022Foundations for learning from noisy quantum experimentscited by 11
  37. 2022Numerical evidence against advantage with quantum fidelity kernels on classical datacited by 11
  38. 2023Quantum neural networks form Gaussian processescited by 11

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