Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

Luo, Di; Chen, Zhuo; Hu, Kaiwen; Zhao, Zhizhen; Hur, Vera Mikyoung; Clark, Bryan K.

doi:10.48550/arxiv.2101.07243

Cited by 22 publications

(23 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, we note that several other papers have studied the importance of using equivariant models applied to different symmetry groups. Luo et al [14] show that gauge equivarant neural networks improve performance on gauge invariant Hamiltonians [13], and Pfau et al [40] use a permutation equivariant model to account for identical electrons. Since many important physics models have substantial symmetry, applications of equivariant models are likely to be important for machine-learning methods in computational physics.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Group Convolutional Neural Networks Improve Quantum State Accuracy

Roth,

MacDonald

2021

Preprint

View full text Add to dashboard Cite

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct symmetry properties. In this paper, we show how to create maximally expressive models for quantum states with specific symmetry properties by drawing on literature from the machine learning community. We implement group equivariant convolutional networks (G-CNN) [1], and demonstrate that performance improvements can be achieved without increasing memory use. We show that G-CNNs achieve very good accuracy for Heisenberg quantum spin models in both ordered and spin liquid regimes, and improve the ground state accuracy on the triangular lattice over other variational Monte-Carlo methods.

show abstract

Section: Discussionmentioning

confidence: 99%

“…This is especially useful on lattice problems which have highly symmetric low-lying energy levels. Recent research [7,[11][12][13][14][15] has shown that forcing neural networks to have the correct symmetry tremendously improves their ability to model the ground state and low-lying excited states of quantum many-body systems.…”

Section: Introductionmentioning

confidence: 99%

Group Convolutional Neural Networks Improve Quantum State Accuracy

Roth,

MacDonald

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…There have been recent successes in enforcing physical symmetries in the architecture of the models themselves. In quantum many-body physics, recent work has shown that the symmetries of quantum energy levels on lattices can be enforced with gauge equivariant and invariant neural networks [15,9,77,51,67,52]. There is significant work on imposing permutation symmetry in jet assignment for high-energy particle collider experiments with self-attention networks [24,46].…”

Section: Universal Approximation Via Linear Invariant Layers and Irre...mentioning

confidence: 99%

Scalars are universal: Equivariant machine learning, structured like classical physics

Villar

Storey-Fisher

Yao

et al. 2021

Preprint

View full text Add to dashboard Cite

There has been enormous progress in the last few years in designing conceivable (though not always practical) neural networks that respect the gauge symmetries-or coordinate freedom-of physical law. Some of these frameworks make use of irreducible representations, some make use of higher order tensor objects, and some apply symmetry-enforcing constraints. Different physical laws obey different combinations of fundamental symmetries, but a large fraction (possibly all) of classical physics is equivariant to translation, rotation, reflection (parity), boost (relativity), and permutations. Here we show that it is simple to parameterize universally approximating polynomial functions that are equivariant under these symmetries, or under the Euclidean, Lorentz, and Poincaré groups, at any dimensionality d. The key observation is that nonlinear O(d)-equivariant (and related-group-equivariant) functions can be expressed in terms of a lightweight collection of scalars-scalar products and scalar contractions of the scalar, vector, and tensor inputs. These results demonstrate theoretically that gauge-invariant deep learning models for classical physics with good scaling for large problems are feasible right now.

show abstract

“…Preservation of gauge symmetries is essential for physical interpretations of the resulting variational state. Recent success in designing symmetry-invariant or equivariant neural states [23,[25][26][27][28][29] has shed light on this difficult task. Research for equivariant variational states with non-Abelian symmetries, or even supersymmetries, however, is still incomplete.…”

Section: Related Workmentioning

confidence: 99%

Neural quantum states for supersymmetric quantum gauge theories

Han¹,

Rinaldi²

2021

Preprint

View full text Add to dashboard Cite

Supersymmetric quantum gauge theories are important mathematical tools in high energy physics. As an example, supersymmetric matrix models can be used as a holographic description of quantum black holes. The wave function of such supersymmetric gauge theories is not known and it is challenging to obtain with traditional techniques. We employ a neural quantum state ansatz for the wave function of a supersymmetric matrix model and use a variational quantum Monte Carlo approach to discover the ground state of the system. We discuss the difficulty of including bosonic particles and fermionic particles, as well as gauge degrees of freedom.Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

show abstract

Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

Cited by 22 publications

References 53 publications

Group Convolutional Neural Networks Improve Quantum State Accuracy

Group Convolutional Neural Networks Improve Quantum State Accuracy

Scalars are universal: Equivariant machine learning, structured like classical physics

Neural quantum states for supersymmetric quantum gauge theories

Contact Info

Product

Resources

About