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Regularization of Riemannian optimization: Application to process tomography and quantum machine learning (2404.19659v1)

Published 30 Apr 2024 in quant-ph

Abstract: Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these gradient descent approaches. Motivated by Lasso regularization, we apply penalties for large ranks of the quantum channel, favoring solutions that can be represented by as few Kraus operators as possible. We apply the method to quantum process tomography and a quantum machine learning problem. Suitably regularized models show faster convergence of the optimization as well as better fidelities in the case of process tomography. Applied to quantum classification scenarios, the regularization terms can simplify the classifying quantum channel without degrading the accuracy of the classification, thereby revealing the minimum channel rank needed for the given input data.

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References (60)
  1. Daniel A. Lidar and Todd A. Brun, editors. “Quantum Error Correction”. Cambridge University Press. Cambridge (2013).
  2. “Roads towards fault-tolerant universal quantum computation”. Nature 549, 172–179 (2017).
  3. John Preskill. “Quantum Computing in the NISQ era and beyond”. Quantum 2, 79 (2018).
  4. “Quantum Error Correction For Dummies” (2023). arxiv:2304.08678.
  5. “Real-time quantum error correction beyond break-even”. Nature 616, 50–55 (2023).
  6. “Measurement-Free Fault-Tolerant Quantum Error Correction in Near-Term Devices”. PRX Quantum 5, 010333 (2024).
  7. John M. Martinis. “Qubit metrology for building a fault-tolerant quantum computer”. npj Quantum Information 1, 1–3 (2015).
  8. “Characterizing large-scale quantum computers via cycle benchmarking”. Nature Communications 10, 5347 (2019).
  9. “Efficient learning of quantum noise”. Nature Physics 16, 1184–1188 (2020).
  10. “Prescription for experimental determination of the dynamics of a quantum black box”. Journal of Modern Optics 44, 2455–2467 (1997).
  11. “Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate”. Physical Review Letters 78, 390–393 (1997).
  12. G. M. D’Ariano and P. Lo Presti. “Quantum Tomography for Measuring Experimentally the Matrix Elements of an Arbitrary Quantum Operation”. Physical Review Letters 86, 4195–4198 (2001).
  13. “Maximum-likelihood estimation of quantum processes”. Physical Review A 63, 020101 (2001).
  14. Massimiliano F. Sacchi. “Maximum-likelihood reconstruction of completely positive maps”. Physical Review A 63, 054104 (2001).
  15. “Quantum process tomography with coherent states”. New Journal of Physics 13, 013006 (2011).
  16. “Maximum-likelihood coherent-state quantum process tomography”. New Journal of Physics 14, 105021 (2012).
  17. “Non-Markovian Quantum Process Tomography”. PRX Quantum 3, 020344 (2022).
  18. “Convex optimization of programmable quantum computers”. npj Quantum Information 6, 1–10 (2020).
  19. “Quantum process tomography via completely positive and trace-preserving projection”. Physical Review A 98, 062336 (2018).
  20. “Projected Least-Squares Quantum Process Tomography”. Quantum 6, 844 (2022).
  21. “Experimental neural network enhanced quantum tomography”. npj Quantum Information 6, 1–5 (2020).
  22. “Quantum process tomography with unsupervised learning and tensor networks”. Nature Communications 14, 2858 (2023).
  23. “Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits”. Nature Physics 6, 409–413 (2010).
  24. “Universal Quantum Gate Set Approaching Fault-Tolerant Thresholds with Superconducting Qubits”. Physical Review Letters 109, 060501 (2012).
  25. “Compressed sensing quantum process tomography for superconducting quantum gates”. Physical Review B 90, 144504 (2014).
  26. “Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits”. Physical Review Applied 14, 024042 (2020).
  27. “Bootstrapping quantum process tomography via a perturbative ansatz”. Nature Communications 11, 1084 (2020).
  28. “Demonstration of non-Markovian process characterisation and control on a quantum processor”. Nature Communications 11, 6301 (2020).
  29. “Quantum Process Tomography of a Controlled-NOT Gate”. Physical Review Letters 93, 080502 (2004).
  30. “Efficient Measurement of Quantum Dynamics via Compressive Sensing”. Physical Review Letters 106, 100401 (2011).
  31. “Process Tomography of Ion Trap Quantum Gates”. Physical Review Letters 97, 220407 (2006).
  32. “Quantum process tomography of the quantum Fourier transform”. The Journal of Chemical Physics 121, 6117–6133 (2004).
  33. “Gradient-descent quantum process tomography by learning kraus operators”. Phys. Rev. Lett. 130, 150402 (2023).
  34. Nicolas Boumal. “An introduction to optimization on smooth manifolds”. Cambridge University Press.  (2023).
  35. “Efficient riemannian optimization on the stiefel manifold via the cayley transform” (2020). arXiv:2002.01113.
  36. “Efficient measurement of quantum dynamics via compressive sensing”. Phys. Rev. Lett. 106, 100401 (2011).
  37. “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators”. New Journal of Physics 14, 095022 (2012).
  38. “Experimental quantum compressed sensing for a seven-qubit system”. Nature Communications 8, 15305 (2017).
  39. Y. S. Teo. “Objective compressive quantum process tomography”. Physical Review A101 (2020).
  40. “QGOpt: Riemannian optimization for quantum technologies”. SciPost Phys. 10, 079 (2021).
  41. “Optimizing quantum circuits with riemannian gradient flow”. Phys. Rev. A 107, 062421 (2023).
  42. “Classification with Quantum Neural Networks on Near Term Processors” (2018) arXiv:1802.06002.
  43. “Power of data in quantum machine learning”. Nature Communications 12, 2631 (2021).
  44. “The Inductive Bias of Quantum Kernels”. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P. S. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems. Volume 34, pages 12661–12673. Curran Associates, Inc. (2021). arXiv:2106.03747.
  45. “A rigorous and robust quantum speed-up in supervised machine learning”. Nature Physics 17, 1013–1017 (2021).
  46. “Is quantum advantage the right goal for quantum machine learning?”. PRX Quantum 3, 030101 (2022).
  47. “Better than classical? the subtle art of benchmarking quantum machine learning models” (2024). arXiv:2403.07059.
  48. Hemant D Tagare. “Notes on Optimization on Stiefel Manifolds”. Online resource (2011).
  49. Robert Tibshirani. “Regression Shrinkage and Selection Via the Lasso”. Journal of the Royal Statistical Society: Series B (Methodological) 58, 267–288 (1996).
  50. “Geometry of Quantum States: An Introduction to Quantum Entanglement”. Cambridge University Press. Cambridge (2006).
  51. Edgar Anderson. “The species problem in iris”. Annals of the Missouri Botanical Garden 23, 457–509 (1936).
  52. Ronald A. Fisher. “The use of multiple measurements in taxonomic problems”. Annals of Eugenics 7, 179–188 (1936).
  53. “Comparative analysis of statistical pattern recognition methods in high dimensional settings”. Pattern Recognition 27, 1065–1077 (1994).
  54. “Quantum machine learning in feature hilbert spaces”. Phys. Rev. Lett. 122, 040504 (2019).
  55. “Effect of data encoding on the expressive power of variational quantum-machine-learning models”. Phys. Rev. A 103, 032430 (2021).
  56. “Robust data encodings for quantum classifiers”. Physical Review A 102, 032420 (2020).
  57. W. Forrest Stinespring. “Positive functions on c*-algebras”. Proceedings of the American Mathematical Society 6, 211–216 (1955).
  58. Francesco Mezzadri. “How to generate random matrices from the classical compact groups” (2007). arXiv:math-ph/0609050.
  59. “Scikit-learn: Machine Learning in Python”. The Journal of Machine Learning Research 12, 2825–2830 (2011).
  60. “Principal component analysis: a review and recent developments”. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 374, 20150202 (2016).

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