(figure adapted from the original jVMC paper arxiv:2108.03409)

jVMC codebase provides a complete framework to calculate time evolution of large 1-D and 2-D open quantum systems using POVMs and neural networks. For simplicity it is assumed that the local Hilbert space dimension of the lattice is $d=2$, i.e., one can only simulate spin-1/2 systems.

This extension allows one to handle dimensions $2< d < 150$ with SIC-POVMs and arbitrary dimensions with orthocross POVM, as well as different local dimensions for the lattice (dimension $d_1$) and some other single-body quantum system, eg. a photonic cavity (dimension $d_2$).

Tomasz Szołdra, Jagiellonian University in Krakow, Poland

A large part of the code is rewritten and adapted from the original jVMC repository.

Tomasz Szołdra is not an author of the original jVMC package. This extension was not officially approved by the creators of the jVMC software. This project is still in the development phase.

• We add an extra lattice site with index $L$ that contains the configuration of the cavity mode. It can have a different local dimension than the lattice sites indexed by $0...(L-1)$.

• Operators are encoded by the following strings where "." is either l (lattice) or c (cavity):

  • 1-body spin: "X_.", "Y_.", "Z_."
  • 1-body bosonic: "a_.", "adag_.", "n_.", "n_.(n_.-1)"
  • 2-body spin: "X_._X_.", "Y_._Y_.", "Z_._Z_.",
  • 2-body lattice-cavity: "Sigma+_l_a_c", "Sigma-_l_adag_c", "X_l_a_c", "X_l_adag_c", "n_l_a_c", "n_l_adag_c", "X_l_X_c", "Y_l_Y_c" "Z_l_Z_c"

• Operators acting on the cavity mode must act on site with index $L$.

• Operators acting on the lattice must act on sites $0...(L-1)$.

For other things, refer to the documentation.

See examples/ folder or an interactive notebook with the toy model of a spin lattice in a dissipative cavity directly at .

• Time evolution of an open system: 1-D lattice and cavity, single- and 2-body terms in the Hamiltonian
• SIC-POVMs for higher dimensions $2 < d < 150$ are supported through the qbsim package.
• Orthocross POVMs for arbitrary local dimension are now supported.
• Spin X, Y, Z operators for arbitrary spin S
• Bosonic creation, annihilation, number operators
• Single-body observables: X, Y, Z and bosonic operators
• Exact and Monte Carlo/autoregressive sampling of the lattice/cavity system

• 2-D systems
• Observables: 2-body correlations
• Operators of arbitrary length
• Complex numbers in the RNN Ansatz
• Documentation

In the original setting, a dense layer with linear activation (blue) is applied to the hidden state of the RNN and the log-probabilities of all configurations are returned. Here, in the presence of cavity, autoregressive sampling is still possible after a slight modification. To support the cavity mode with a different local dimension, another independent dense multilayer perceptron (MLP, red) is added. Last layer of the MLP has linear activation. $\mathbf{a}$ is the configuration of the lattice and cavity together.

There is another linear dense layer at the input to the LSTM/RNN (pink in the picture).

1. We recommend you create a new conda environment to work with jVMC_cavity:

    conda create -n jvmc_cavity python=3.9
    conda activate jvmc_cavity
    conda install pip
    pip install --upgrade pip
   

2. [Optional] For GPU support:

    conda install -c conda-forge cudatoolkit=11.8
    export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$CONDA_PREFIX/lib/
    mkdir -p $CONDA_PREFIX/etc/conda/activate.d
    echo 'export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$CONDA_PREFIX/lib/' > $CONDA_PREFIX/etc/conda/activate.d/env_vars.sh
   

3. Install two packages manually with conda:

    conda install -c conda-forge mpi4py openmpi
   

4. Install jVMC:

    pip install jVMC
   

5. Download the package

    git clone https://github.com/tszoldra/jVMC_cavity
   

6. pip-install the package

    pip install jVMC_cavity
   

7. [Optional] For GPU support:

    pip install "jax[cuda12_pip]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html
    pip install --upgrade flax