Abstract
Inspired by proposals for continuous-variable quantum approximate optimization (CV-QAOA), we investigate the utility of continuous-variable neural network quantum states (CV-NQS) for performing continuous optimization, focusing on the ground state optimization of the classical antiferromagnetic rotor model. Numerical experiments conducted using variational Monte Carlo with CV-NQS indicate that although the non-local algorithm succeeds in finding ground states competitive with the local gradient search methods, the proposal suffers from unfavorable scaling. A number of proposed extensions are put forward which may help alleviate the scaling difficulty.
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Acknowledgements
We thank James Stokes (Flatiron Institute) for many helpful discussions. This research was supported in part through computational resources and services provided by UM’s Advanced Research Computing.
Funding
This research received support from the Automotive Research Center at the University of Michigan (UM) in accordance with Cooperative Agreement W56HZV-19-2-0001 with U.S. Army DEVCOM Ground Vehicle Systems Center.
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Appendix: NQS applied to simple graphs
Appendix: NQS applied to simple graphs
In this section, we consider a collection of Max-Cut problems defined on simple and/or small graphs for which the optimal solution can be obtained easily via brute force search. The graphs, optimal cut value, and the cut value obtained by the NQS approach coupled with the Procedure-Cut algorithm for converting continuous-variable solution to cut are given in Table 5. For graphs with 4 nodes, we use Niter = 300, Nsamp = 10, Nwarm = 0 and λreg = 10− 9. For graphs with 6 nodes, we use Niter = 1000, Nsamp = 40, Nwarm = 0 and λreg = 10− 9. For graphs with 12 nodes, we use Niter = 4000, Nsamp = 40, Nwarm = 0 and λreg = 10− 9. Note that the observed standard deviation for the 10 runs (each with a different random seed) for all the tests cases is zero. This suggests that for simple graphs with appropriate parameter choices the NQS approach, although being Stochastic in nature, always gives the rotor configurations that leads to the optimal cut value for the graphs.
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Zhang, Y., Gorsich, D., Jayakumar, P. et al. Continuous-variable optimization with neural network quantum states. Quantum Mach. Intell. 4, 9 (2022). https://doi.org/10.1007/s42484-022-00067-z
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DOI: https://doi.org/10.1007/s42484-022-00067-z