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RydbergGPT

A large language model (LLM) for Rydberg atom array physics. Manuscript available on arXiv.

Architecture

Rydberg System

\[ \hat{H}_{\mathrm{Rydberg}} = \sum_{i < j}^{N} \frac{C_6}{\lVert \mathbf{r}_i - \mathbf{r}_j \rVert} \hat{n}_i \hat{n}_j - \delta \sum_{i}^{N} \hat{n}_i - \frac{\Omega}{2} \sum_{i}^{N} \hat{\sigma}_i^{(x)}, \]
\[ C_6 = \Omega \left( \frac{R_b}{a} \right)^6, \quad V_{ij} = \frac{a^6}{\lVert \mathbf{r}_i - \mathbf{r}_j \rVert^6} \]
  • \(N = L \times L =\) number of atoms/qubits
  • \(i, j =\) qubit index
  • \(V_{ij} =\) blockade interaction between qubits \(i\) and \(j\)
  • \(a =\) Lattice spacing
  • \(R_b =\) Rydberg blockade radius
  • \(\mathbf{r}_i =\) the position of qubit \(i\)
  • \(\hat{n}_i =\) number operator at qubit \(i\)
  • \(\delta =\) detuning at qubit \(i\)
  • \(\Omega =\) Rabi frequency at qubit \(i\)
  • \(\beta =\) Inverse temperature of system

Transformer

Vanilla transformer architecture taken from Attention is All You Need.

Architecture

  • \(\mathbf{x} =\) experimental settings
  • \(\sigma_i =\) one-hot encoding of measured qubit \(i\)
  • \(p_{\theta}(\sigma_i | \sigma_{< i}) =\) neural network conditional probability distribution of qubit \(i\)

The transformer encoder represents the Rydberg Hamiltonian with a sequence.
The transformer decoder represents the corresponding ground state wavefunction.

Acknowledgements

We sincerely thank the authors of the following very helpful codebases we used when building this repository :

References

@inproceedings{46201,
title   = {Attention is All You Need},
author  = {Ashish Vaswani and Noam Shazeer and Niki Parmar and Jakob Uszkoreit and Llion Jones and Aidan N. Gomez and Lukasz Kaiser and Illia Polosukhin},
year    = {2017},
URL = {https://arxiv.org/pdf/1706.03762.pdf}
}