Many-body localized hidden generative models (2207.02346v3)
Abstract: Born machines are quantum-inspired generative models that leverage the probabilistic nature of quantum states. Here, we present a new architecture called many-body localized (MBL) hidden Born machine that utilizes both MBL dynamics and hidden units as learning resources. We show that the hidden units act as an effective thermal bath that enhances the trainability of the system, while the MBL dynamics stabilize the training trajectories. We numerically demonstrate that the MBL hidden Born machine is capable of learning a variety of tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and non-local parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources, and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems.
- P. Ball et al., Nature 599, 542 (2021).
- D. Marković and J. Grollier, Applied Physics Letters 117, 150501 (2020).
- E. Torrontegui and J. J. García-Ripoll, EPL (Europhysics Letters) 125, 30004 (2019).
- K. Fujii and K. Nakajima, in Reservoir Computing (Springer, 2021) pp. 423–450.
- A. M. Gomez, S. F. Yelin, and K. Najafi, “Reconstructing quantum states using basis-enhanced born machines,” (2022).
- J.-G. Liu and L. Wang, Physical Review A 98, 062324 (2018).
- P. Smolensky, Information processing in dynamical systems: Foundations of harmony theory, Tech. Rep. (Colorado Univ at Boulder Dept of Computer Science, 1986).
- G. E. Hinton and R. R. Salakhutdinov, science 313, 504 (2006).
- X. Gao and L.-M. Duan, Nature communications 8, 1 (2017).
- J. J. Hopfield, Proceedings of the national academy of sciences 79, 2554 (1982).
- D. Krotov and J. J. Hopfield, Advances in neural information processing systems 29 (2016).
- J. M. Deutsch, Phys. Rev. A 43, 2046 (1991).
- M. Srednicki, Physical Review E 50, 888 (1994).
- P. W. Anderson, Phys. Rev. 109, 1492 (1958).
- V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).
- A. Pal and D. A. Huse, Phys. Rev. B 82, 174411 (2010).
- T. Devakul and R. R. P. Singh, Phys. Rev. Lett. 115, 187201 (2015).
- L. Bottou et al., Proceedings of Neuro-Nımes 91, 12 (1991).
- L. Deng, IEEE Signal Processing Magazine 29, 141 (2012).
- P. Hauke and M. Heyl, Physical Review B 92 (2015), 10.1103/physrevb.92.134204.
- E. Winfree, Algorithmic self-assembly of DNA (California Institute of Technology, 1998).
- J. O’Brien and A. Murugan, ACS Synthetic Biology 8, 826 (2019).
- M. Stern and A. Murugan, arXiv preprint arXiv:2206.05831 (2022).
- While there exists other more sophisticated encoding schemes, here we choose the simplest one for illustration.
- A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, “The randomized measurement toolbox,” (2022).
- R. Movassagh, Nature Physics , 1 (2023).
- P. Weinberg and M. Bukov, SciPost Physics 2, 003 (2017).
- P. Weinberg and M. Bukov, SciPost Physics 7, 020 (2019).
- R. Nandkishore and D. A. Huse, arXiv preprint arXiv:1404.0686 (2014).
- F. Alet and N. Laflorencie, Comptes Rendus Physique 19, 498 (2018).