Efficient representation of quantum many-body states with deep neural networks

By Xun Gao, Luming Duan. Nature Communications, 2017

401 citations recorded by the source corpus.

Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states. One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/3378a002a26dcacc7a68cb25fefc6ee5424ca02f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Hsin-Yuan Huang
2. Richard Kueng
3. John Preskill
4. J. I. Cirac
5. Vedran Dunjko
6. Ruimeng Hu
7. Hans J. Briegel
8. Marin Bukov

In Atomic and Molecular Physics, and Optics

1. Hsin-Yuan Huang
2. Hans J. Briegel
3. Vedran Dunjko
4. Richard Kueng
5. John Preskill
6. David J. Schwab
7. J. I. Cirac
8. Iván Díaz de León Rodríguez

In Materials Chemistry

1. Vedran Dunjko
2. Hans J. Briegel
3. Richard Kueng
4. John Preskill
5. Hsin-Yuan Huang
6. Jiequn Han
7. Shuo-Hui Li
8. Lei Wang

Citations in the corpus

• Predicting many properties of a quantum system from very few measurements (2020, methodology): “[29] X.”
• Thermodynamics (2021, neutral): “While it seems unlikely that this can be done in general, deep neural networks could possibly lead to a better representation of such states and thus alleviate this issue to some degree [57].”
• Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games (2019, background): “…in numerical computation, ranging from artificial intelligence (cf. Bengio (2009); LeCun et al. (2015)) such as computer vision and speech recognition, to scientific computing (see e.g., Carleo and Troyer (2017); Gao and Duan (2017); Han et al. (2018); Zhang et al. (2018b); Han et al. (2019)).”
• Machine learning \& artificial intelligence in the quantum domain (2017, background): “represent ground states of any k-local Hamiltonians with polynomial-size gaps (Gao and Duan, 2017).”
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States (2017, methodology): “[90] I. Glasser, J. I. Cirac, G. Sierra, and A. E. B. Nielsen, “Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models,” New J. Phys.”
• A high-bias, low-variance introduction to Machine Learning for physicists (2018, positive): “Representing quantum states as DNNs (Gao et al., 2017; Gao and Duan, 2017; Levine 46 et al., 2017; Saito and Kato, 2017) and quantum state tomography (Torlai et al., 2017) are among some of the impressive achievements to reveal the potential of DNNs to facilitate the study of quantum systems.”