Deep recurrent networks predicting the gap evolution in adiabatic quantum computing

Naeimeh Mohseni1,2, Carlos Navarrete-Benlloch3,4,1, Tim Byrnes5,6,7,8,9, and Florian Marquardt1,2

1Max-Planck-Institut für die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany
2Physics Department, University of Erlangen-Nuremberg, Staudtstr. 5, 91058 Erlangen, Germany
3Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
4Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
5New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China
6State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences,East China Normal University, Shanghai 200062, China
7NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
8Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi, UAE
9Department of Physics, New York University, New York, NY 10003, USA

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In adiabatic quantum computing finding the dependence of the gap of the Hamiltonian as a function of the parameter varied during the adiabatic sweep is crucial in order to optimize the speed of the computation. Inspired by this challenge, in this work we explore the potential of deep learning for discovering a mapping from the parameters that fully identify a problem Hamiltonian to the aforementioned parametric dependence of the gap applying different network architectures. Through this example, we conjecture that a limiting factor for the learnability of such problems is the size of the input, that is, how the number of parameters needed to identify the Hamiltonian scales with the system size. We show that a long short-term memory network succeeds in predicting the gap when the parameter space scales linearly with system size. Remarkably, we show that once this architecture is combined with a convolutional neural network to deal with the spatial structure of the model, the gap evolution can even be predicted for system sizes larger than the ones seen by the neural network during training. This provides a significant speedup in comparison with the existing exact and approximate algorithms in calculating the gap.

In the field of adiabatic quantum computing, one key aspect for achieving optimal computation speed is to understand how the gap of the Hamiltonian depends on the varied parameters during the adiabatic sweep. Motivated by this challenge, our paper embarks on investigating the potential of deep learning techniques to discover a mapping between problem Hamiltonian parameters and the parametric dependence of the gap. By employing diverse network architectures, we investigate the learnability limits of such problems. Our investigation suggests that the scalability of the number of parameters needed to identify the Hamiltonian with respect to the system size plays a critical role in the learnability of such problems.

Remarkably, we show that a trained neural network succeeds in predicting the full gap evolution during an adiabatic sweep for large system sizes just by having it observe the gap for small system sizes, given the parameter space scales linearly with system size. Our study adds up to the promise of so-called convolutional recurrent networks in predicting the adiabatic dynamics of inhomogeneous many-body systems and their potential for extrapolating the dynamics beyond what the neural network is trained on.

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Cited by

[1] Pratibha Raghupati Hegde, Gianluca Passarelli, Giovanni Cantele, and Procolo Lucignano, "Deep learning optimal quantum annealing schedules for random Ising models", New Journal of Physics 25 7, 073013 (2023).

[2] Naeimeh Mohseni, Peter L. McMahon, and Tim Byrnes, "Ising machines as hardware solvers of combinatorial optimization problems", Nature Reviews Physics 4 6, 363 (2022).

[3] Naeimeh Mohseni, Thomas Fösel, Lingzhen Guo, Carlos Navarrete-Benlloch, and Florian Marquardt, "Deep Learning of Quantum Many-Body Dynamics via Random Driving", Quantum 6, 714 (2022).

[4] Alexander Gresch, Lennart Bittel, and Martin Kliesch, "Scalable approach to many-body localization via quantum data", arXiv:2202.08853, (2022).

[5] Naeimeh Mohseni, Junheng Shi, Tim Byrnes, and Michael Hartmann, "Deep learning of many-body observables and quantum information scrambling", arXiv:2302.04621, (2023).

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