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Dequantizing algorithms to understand quantum advantage in machine learning

Understanding whether quantum machine learning algorithms present a genuine computational advantage over classical approaches is challenging. Ewin Tang explains how dequantizing algorithms can uncover when there is no quantum speedup and perhaps help explore analogies between quantum and classical linear algebra.

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References

  1. Kerenidis, I. & Prakash, A. Quantum recommendation systems. In Proc. 8th Innovations Theor. Comput. Sci. Conf. (ITCS) 49:1–49:21 (Schloss Dagstuhl, 2017).

  2. Lloyd, S., Garnerone, S. & Zanardi, P. Quantum algorithms for topological and geometric analysis of data. Nat. Commun. 7, 10138 (2016).

    Article  ADS  Google Scholar 

  3. Aaronson, S. Read the fine print. Nat. Phys. 11, 291–293 (2015).

    Article  Google Scholar 

  4. Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  5. Chia, N.-H. et al. Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning. In Proc. 52nd Ann. ACM SIGACT Symp. Theory of Comput. (STOC 2020) 387–400 (Association for Computing Machinery, 2020).

  6. Gharibian, S. & Le Gall, F. Dequantizing the quantum singular value transformation: Hardness and applications to quantum chemistry and the quantum PCP conjecture. In Proc. 54th Ann. ACM SIGACT Symp. Theory of Comput. (STOC 2022) 19–32 (Association for Computing Machinery, 2022).

  7. Woodruff, D. P. Sketching as a tool for numerical linear algebra. Found. Trends Theor. Comput. Sci. 10, 1–157 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  8. Drineas, P., Kannan, R. & Mahoney, M. W. Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix. SIAM J. Comput. 36, 158–183 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  9. Cotler, J., Huang, H.-Y. & McClean, J. R. Revisiting dequantization and quantum advantage in learning tasks. Preprint at https://arxiv.org/abs/2112.00811 (2021).

  10. Huang, H.-Y. et al. Quantum advantage in learning from experiments. Science 376, 1182–1186 (2022).

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Correspondence to Ewin Tang.

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Tang, E. Dequantizing algorithms to understand quantum advantage in machine learning. Nat Rev Phys 4, 692–693 (2022). https://doi.org/10.1038/s42254-022-00511-w

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