Neural quantum solver for excited states of trapped ion quantum computing

This repository contains the code and data for the paper Solving excited states for long-range interacting trapped ions with neural networks.

Organization

• code/Jmat/code/Ising2d_power_law.py: Python code to generate the interactive Hamiltonian (the J_ij matrix) for the trapped ion model
• code/rbm.cc: Optimized C++ code for the neural quantum solver with and without the matrix-free method. This is the code that generated the data in the paper
• data/energy: Energy spectrum generated at each step of the training process
• data/corrfcn: Data for the correlation functions
• data/rbm-weights: Weights of the RBM neural networks at the end of the training process

Building and running the code

To build the code, change directory to code and simply run

./build.sh [opt]

Without opt, the default is to generate debug builds which are unoptimized and contain all the debugging information. With opt, the compiler will be instructed to generate optimized code without debugging symbols in the executable.

To run the code, use the script run.sh. For instance,

./run.sh ./rbm-matfree-N32-M64-K2-opt -c 128 --model trappedion -h 0.595 -n 200 -m 200 --tol 1e-6 --reglam-init 40 --reglam-cutoff 1 --minres-rtol 1e-9 --correlation-data ioncorrN32M64K2h0.595.mat --dump-rbm ionh0.595

will perform a simulation of 32 trapped ions using RBM states with 64 hidden units, and solve for the two lowest energy states in the spectrum, using the optimized matrix-free method. RBM weights are correlation function data will be stored to the specified MATLAB .mat files. For a complete list of supported command line parameters, do

./rbm-matfree-N32-M64-K2-opt -?

To build additional executables for different combinations of N, M, and K, change the line in the build script

PARAMS=("8 16 2" ...)

to the parameters you want. The format is "N M K", in this order. For instance, to build the executable for an RBM solver with N=10, M=20, K=3, do

PARAMS=("10 20 3")

If the specified N is not in the list of pre-built J matrices, you must generate the corresponding J matrix using the code supplied under code/Jmat/code. Simply specify N as the parameter to the script, for instance,

python Ising2d_power_law.py 10

if you want to generate the J matrix for the trapped ion model with N=10 ions.

Data format

Data under data/energy are text files listing the energy spectrum at each step of the training processes. Data under data/corrfcn and data/rbm-weights are matrices stored in the MATLAB .mat file (version 5), which can be processed using standard tools such as python's scipy package.

Citing our paper

@misc{Ma2025Solving,
  title = {Solving Excited States for Long-Range Interacting Trapped Ions with Neural Networks},
  author = {Yixuan Ma and Chang Liu and Weikang Li and Shun-Yao Zhang and L. -M. Duan and Yukai Wu and Dong-Ling Deng},
  year = {2025},
  number = {arXiv:2506.08594},
  eprint = {2506.08594},
  primaryclass = {quant-ph},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2506.08594},
  archiveprefix = {arXiv}
}