Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 71 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 12 tok/s Pro
GPT-5 High 21 tok/s Pro
GPT-4o 81 tok/s Pro
Kimi K2 231 tok/s Pro
GPT OSS 120B 435 tok/s Pro
Claude Sonnet 4 33 tok/s Pro
2000 character limit reached

Quantum Shadow Gradient Descent for Variational Quantum Algorithms (2310.06935v2)

Published 10 Oct 2023 in quant-ph and cs.LG

Abstract: Gradient-based optimizers have been proposed for training variational quantum circuits in settings such as quantum neural networks (QNNs). The task of gradient estimation, however, has proven to be challenging, primarily due to distinctive quantum features such as state collapse and measurement incompatibility. Conventional techniques, such as the parameter-shift rule, necessitate several fresh samples in each iteration to estimate the gradient due to the stochastic nature of state measurement. Owing to state collapse from measurement, the inability to reuse samples in subsequent iterations motivates a crucial inquiry into whether fundamentally more efficient approaches to sample utilization exist. In this paper, we affirm the feasibility of such efficiency enhancements through a novel procedure called quantum shadow gradient descent (QSGD), which uses a single sample per iteration to estimate all components of the gradient. Our approach is based on an adaptation of shadow tomography that significantly enhances sample efficiency. Through detailed theoretical analysis, we show that QSGD has a significantly faster convergence rate than existing methods under locality conditions. We present detailed numerical experiments supporting all of our theoretical claims.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (56)
  1. Aaronson, S. 2018. Shadow Tomography of Quantum States. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, 325–338. New York, NY, USA: Association for Computing Machinery. ISBN 9781450355599.
  2. Quantum Algorithms for Quantum Chemistry and Quantum Materials Science. Chemical Reviews, 120(22): 12685–12717.
  3. Training deep quantum neural networks. Nature Communications, 11(1).
  4. Quantum machine learning. 549(7671): 195–202.
  5. Optimization Methods for Large-Scale Machine Learning.
  6. Machine learning quantum phases of matter beyond the fermion sign problem. 7(1).
  7. TensorFlow Quantum: A Software Framework for Quantum Machine Learning. arXiv:2003.02989.
  8. Quantum Chemistry in the Age of Quantum Computing. Chemical Reviews, 119(19): 10856–10915.
  9. Solving the quantum many-body problem with artificial neural networks. 355(6325): 602–606.
  10. Machine learning phases of matter. 13(5): 431–434.
  11. Variational Quantum Algorithms. arXiv:2012.09265.
  12. Entanglement structure detection via machine learning. Quantum Science and Technology.
  13. Universal discriminative quantum neural networks.
  14. Quantum entanglement in neural network states. Physical Review X, 7(2): 021021.
  15. A Quantum Approximate Optimization Algorithm. arXiv:1411.4028.
  16. Classification with Quantum Neural Networks on Near Term Processors.
  17. Optimizing quantum optimization algorithms via faster quantum gradient computation. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, 1425–1444. Society for Industrial and Applied Mathematics.
  18. Quantum Random Access Memory. Physical Review Letters, 100(16).
  19. Practical optimization for hybrid quantum-classical algorithms. arXiv:1701.01450.
  20. Low-Depth Gradient Measurements Can Improve Convergence in Variational Hybrid Quantum-Classical Algorithms. Physical Review Letters, 126(14): 140502.
  21. Toward Physically Realizable Quantum Neural Networks. Association for the Advancement of Articial Intelligence (AAAI).
  22. A Theoretical Framework for Learning from Quantum Data. In IEEE International Symposium on Information Theory (ISIT).
  23. Learning k-qubit Quantum Operators via Pauli Decomposition. In Ruiz, F.; Dy, J.; and van de Meent, J.-W., eds., Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, volume 206 of Proceedings of Machine Learning Research. PMLR.
  24. Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator. Physical Review X, 8(3): 031022.
  25. Hiesmayr, B. C. 2021. Free versus bound entanglement, a NP-hard problem tackled by machine learning. Scientific Reports, 11(1).
  26. Holevo, A. S. 2012. Quantum Systems, Channels, Information. DE GRUYTER.
  27. Predicting Many Properties of a Quantum System from Very Few Measurements. Nature Physics 16, 1050–1057 (2020).
  28. Johnston, N. 2016. QETLAB: A MATLAB toolbox for quantum entanglement, version 0.9. http://qetlab.com.
  29. Parametrized Hamiltonian simulation using quantum optimal control. Physical Review A, 104(4): 042602.
  30. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671): 242–246.
  31. Simulating Chemistry Using Quantum Computers. Annual Review of Physical Chemistry, 62(1): 185–207.
  32. Lewenstein, M. 1994. Quantum perceptrons. Journal of Modern Optics, 41(12): 2491–2501.
  33. VSQL: Variational Shadow Quantum Learning for Classification. Proceedings of the AAAI Conference on Artificial Intelligence, 35(9): 8357–8365.
  34. How Does Noise Help Robustness? Explanation and Exploration under the Neural SDE Framework. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 279–287.
  35. Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411.
  36. Quantum principal component analysis. 10(9): 631–633.
  37. Separability-entanglement classifier via machine learning. Physical Review A, 98(1): 012315.
  38. Transforming Bell’s inequalities into state classifiers with machine learning. npj Quantum Information, 4(1).
  39. A Leap among Entanglement and Neural Networks: A Quantum Survey. arXiv:2107.03313.
  40. Quantum computational chemistry. Reviews of Modern Physics, 92(1): 015003.
  41. Michael A. Nielsen, I. L. C. 2010. Quantum Computation and Quantum Information. Cambridge University Pr. ISBN 1107002176.
  42. Quantum algorithms for quantum dynamics: A performance study on the spin-boson model. Physical Review Research, 3(4): 043212.
  43. Quantum circuit learning. Physical Review A, 98(3): 032309.
  44. Optical Realization of Optimal Unambiguous Discrimination for Pure and Mixed Quantum States. Physical Review Letters, 93(20): 200403.
  45. Circuit-Based Quantum Random Access Memory for Classical Data. Scientific Reports, 9(1).
  46. Quantum state discrimination using noisy quantum neural networks. Physical Review Research, 3(1): 013063.
  47. Quantum Support Vector Machine for Big Data Classification. Physical Review Letters, 113(13).
  48. Evaluating analytic gradients on quantum hardware. Phys. Rev. A 99, 032331 (2019).
  49. Circuit-centric quantum classifiers. Physical Review A, 101(3): 032308.
  50. The quest for a Quantum Neural Network. Quantum Information Processing, 13(11): 2567–2586.
  51. Understanding Machine Learning: From Theory to Algorithms. New York, NY, USA: Cambridge University Press. ISBN 1107057132, 9781107057135.
  52. Suzuki, M. 1976. Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Communications in Mathematical Physics, 51(2): 183–190.
  53. Stochastic gradient descent for hybrid quantum-classical optimization. Quantum, 4: 314.
  54. Unitary quantum perceptron as efficient universal approximator. EPL 125 30004, (2019).
  55. Quantum cellular neural networks. Superlattices and Microstructures, 20(4): 473–478.
  56. Improved quantum computing with higher-order Trotter decomposition. Physical Review A, 106(4): 042401.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up