Empowering deep neural quantum states through efficient optimization
arXiv:2302.01941
Ao Chen and Markus Heyl
University of Augsburg
Why neural �quantum states?
Image recognition
Input image
Model
0.98
0.12
Game of go
Game status
Model
0.12
Quantum many-body
Model
0.41
-0.25
First step
G. Carleo, & M. Troyer, Science (2017)
Past five years
Frustrated J1-J2 model
K. Choo, T. Neupert & G. Carleo, Phys. Rev. B (2019)
Method | Energy |
CNN | |
DMRG | |
Traditional VMC | |
Ground state | |
Convolutional neural network (CNN)
NQS can’t learn signs?
24-site Kagome J1-J2
T. Westerhout, et al., Nat. Commun. (2020)
Method | Energy |
CNN | |
Simple sign rule limit | |
Traditional VMC | |
Ground state | |
DON’T separate amplitudes and signs
Z. Cai & J. Liu, Phys. Rev. B (2018)
A. Szabó & C. Castelnovo, Phys. Rev. Res. (2020)
M. Bukov, M. Schmitt & M. Dupont, SciPost Phys. (2021)
A. Chen, et al., Phys. Rev. Res. (2022)
G. Torlai, et al., Nat. Phys. (2018)
Network design
Autoregressive network
O. Sharir, et al., Phys. Rev. Lett. (2020)
Recurrent neural network (RNN)
M. Hibat-Allah, et al., Phys. Rev. Res. (2020)
Symmetry projection
Y. Normura, J. Phys.: Condens. Matter (2021)
M. Reh, M. Schmitt & M. Gärttner, Phys. Rev. B (2023)
Group convolutional neural network (GCNN)
C. Roth, A. Szabó & A. H. MacDonald, Phys. Rev. B (2023)
Vision transformer (ViT)
L. L. Viteritti, R. Rende & F. Becca, Phys. Rev. Lett. (2023)
More �(parameters) �is different
Deeper NQS
Method | Energy |
CNN | |
Simple sign rule limit | |
| |
Traditional VMC | |
Ground state | |
M. Li, et al., IEEE TPDS (2022)
Deep Boltzmann machine
X. Gao & L. Duan, Nat. Commun. (2017)
G. Carleo, Y. Nomura, M. Imada, Nat. Commun. (2018)
Optimization
Stochastic gradient descent (SGD)
Stochastic reconfiguration (SR)
MinSR
Benchmark model
Method | Energy |
CNN | |
Traditional VMC | |
Deep CNN (MinSR) | |
Ground state | |
Application: �quantum spin liquids
Energy gap of quantum spin liquids
Y. Nomura & M. Imada, Phys. Rev. X (2021)
Y. Iqbal, et al., Phys. Rev. B (2016)
Structure factor
Summary
Sign structure
Network design
MinSR
Fermionic lattice
Y. Nomura, et al., Phys. Rev. B (2017)
D. Luo & B. K. Clark, Phys. Rev. Lett. (2019)
J. R. Moreno, et al., PNAS (2022)
Quantum spin liquid
Y. Nomura & M. Imada, Phys. Rev. X (2021)
Quantum chemistry
J. Hermann, et al., Nat. Rev. Chem. (2023)
Quantum dynamics
M. Schmitt & M. Heyl, Phys. Rev. Lett. (2020)
A. Sinibaldi, et al., Quantum (2023)
J. Hermann, et al., Nat. Chem. (2020)
D. Pfau, et al., Phys. Rev. Res. (2020)
Encoding physical backgrounds
Y. Nomura, et al., Phys. Rev. B (2017)
Z. Chen, et al., NIPS (2023)
More...
Thank you!