Meta-variational quantum Monte Carlo
Tóm tắt
Motivated by close analogies between meta-reinforcement learning (Meta-RL) and variational quantum Monte Carlo with disorder, we propose a learning problem and an associated notion of generalization, with applications in ground state determination for quantum systems described by random Hamiltonians. Specifically, we elaborate on a proposal of (Zhao et al. 2020b) interpreting the Hamiltonian disorder as task uncertainty for a Meta-RL agent. A model-agnostic meta-learning approach is proposed to solve the associated learning problem and numerical experiments in disordered quantum spin systems indicate that the resulting meta-variational Monte Carlo accelerates training and improves converged energies.
Tài liệu tham khảo
Andrychowicz M, Denil M, Gomez S, Hoffman MW, Pfau D, Schaul T, Shillingford B, De Freitas N (2016) Learning to learn by gradient descent by gradient descent. In: Advances in neural information processing systems
Baxter J (2000) A model of inductive bias learning. J Artif Intell Res 12:149–198
Carleo G, Troyer M (2017) Solving the quantum many-body problem with artificial neural networks. Science 355(6325):602–606
Caruana R (1997) Multitask learning. Mach Learn 28(1):41–75
Fallah A, Mokhtari A, Ozdaglar A (2020) On the convergence theory of gradient-based model-agnostic meta-learning algorithms. In: International conference on artificial intelligence and statistics, pp 1082–1092
Finn C, Abbeel P, Levine S (2017) Model-agnostic meta-learning for fast adaptation of deep networks. In: Proceedings of the 34th international conference on machine learning. JMLR. org, vol 70, pp 1126–1135
Flennerhag S, Rusu AA, Pascanu R, Visin F, Yin H, Hadsell R (2019) Meta-learning with warped gradient descent. arXiv:1909.00025
Gomes J, McKiernan KA, Eastman P, Pande VS (2019) Classical quantum optimization with neural network quantum states. arXiv:1910.10675
Kakade SM (2001) A natural policy gradient. Adv Neural Inf process Syst 14
Luo D, Clark BK (2019) Backflow transformations via neural networks for quantum many-body wave functions. Phys Rev Lett 122(22):226401
McCloskey M, Cohen NJ (1989) Catastrophic interference in connectionist networks: the sequential learning problem. In: Psychology of learning and motivation, vol 24, pp 109–165
McMillan WL (1965) Ground state of liquid he4. Phys Rev 138:442–451
Nichol A, Achiam J, Schulman J (2018) On first-order meta-learning algorithms. arXiv:1803.02999
Nomura Y, Darmawan AS, Yamaji Y, Imada M (2017) Restricted Boltzmann machine learning for solving strongly correlated quantum systems. Phys Rev B 96(20):205152
Pfau D, Spencer JS, Matthews AG, Foulkes WMC (2020) AB initio solution of the many-electron Schrödinger equation with deep neural networks. Phys Rev Res 2(3):033429
Rendl F, Rinaldi G, Wiegele A (2010) Solving max-cut to optimality by intersecting semidefinite and polyhedral relaxations. Math Program 121(2):307
Sharir O, Levine Y, Wies N, Carleo G, Shashua A (2020) Deep autoregressive models for the efficient variational simulation of many-body quantum systems. Phys Rev Lett 124(2):020503
Sorella S (1998) Green function Monte Carlo with stochastic reconfiguration. Phys Rev Lett 80 (20):4558–4561
Stokes J, Moreno JR, Pnevmatikakis EA, Carleo G (2020) Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states. Phys Rev B 102(20):205122
Thrun S, Pratt L (2012) Learning to learn. Springer Science and Business Media, Berlin
Verdon G, Broughton M, McClean JR, Sung KJ, Babbush R, Jiang Z, Neven H, Mohseni M (2019) Learning to learn with quantum neural networks via classical neural networks. arXiv:1907.05415
Wierstra D, Schaul T, Glasmachers T, Sun Y, Peters J, Schmidhuber J (2014) Natural evolution strategies. J Mach Learn Res 15(1):949–980
Williams R (1988) Toward a theory of reinforcement-learning connectionist systems. Technical Report NU-CCS-88-3 Northeastern University
Williams RJ (1992) Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach Learn 8(3):229–256
Wilson M, Stromswold R, Wudarski F, Hadfield S, Tubman NM, Rieffel EG (2021) Optimizing quantum heuristics with meta-learning. Quantum Mach Intell 3(1):1–14
Zhao T, Carleo G, Stokes J, Veerapaneni S (2020a) Natural evolution strategies and variational Monte Carlo. Mach Learn Sci Technol 2(2):02–01
Zhao T, Stokes J, Knitter O, Chen B, Veerapaneni S (2020b) Meta variational Monte Carlo. Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020)
Zhao T, De S, Chen B, Stokes J, Veerapaneni S (2021) Overcoming barriers to scalability in variational quantum Monte Carlo. In: The international conference for high performance computing, networking, storage, and analysis