Bosonic and Supersymmetric BMN models solved with QISKIT

Use the Variational Quantum Eigensolver in QISKIT to find the ground state of the quantum 2-matrix model with gauge group SU(2) at different 't Hooft couplings. We consider a purely bosonic model and a supersymmetric model (minimal BMN). Results are reported in the publication Rinaldi et al. (2021). Consider the citation in Cite.

Code

Installation

Install the conda environment manager for python and create a new environment for this project:

conda env create -f environment.yml

This will install a new python environment with the dependencies needed to run QISKIT and the scripts and notebooks of this repository. Check that the environment exists

conda env list

and then activate it

conda activate qiskit-env

Scripts

For making plots and datafiles, you can also use the python scripts in the scripts folder.

The file qiskit.ini contains QISKIT setting. You can copy it to your default location usually found in ${HOME}/.qiskit/settings.conf.

Running main scripts with -h will let you see the command line options, e.g.

python script/01_bmn2_bosonic_VQE.py -h

or

python script/02_bmn2_mini_VQE.py -h

The data produced is saved in the data folder using the binary HDF5 protocol (with one command line flag you can save in pickle compressed format).

Note: You can run on multiple threads by using i.e.

export OMP_NUM_THREADS=6; python scripts/02_bmn2_mini_VQE.py --L=2 --N=2 --g2N=0.2 --optimizer='COBYLA' --varform=['ry','rz'] --depth=3 --nrep=10

The scripts/hokusai folder is for scripts managing the submission of jobs on the RIKEN Hokusai cluster in Wako, Japan.

There are also utility scripts for making plots.

Notebooks

The notebooks in notebooks can be used as a starting point to understand the code.

• The notebook QISKIT_HarmonicOscillator_VQE.ipynb gives an introduction to the VQE for a simple harmonic oscillator in the coordinate basis.
• The notebook QISKIT_bosonic_matrices_VQE.ipynb gives an introduction to the VQE for the bosonic quantum matrix model.
• The notebook QISKIT_susy_matrices_VQE.ipynb gives an introduction to the VQE for the supersymmetric quantum matrix model.

Cite

If you use this code (or parts of it), please consider citing our paper:

@article{Rinaldi:2021jbg,
    author = "Rinaldi, Enrico and Han, Xizhi and Hassan, Mohammad and Feng, Yuan and Nori, Franco and McGuigan, Michael and Hanada, Masanori",
    title = "{Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo}",
    eprint = "2108.02942",
    archivePrefix = "arXiv",
    primaryClass = "quant-ph",
    reportNumber = "RIKEN-iTHEMS-Report-21, DMUS-MP-21/10",
    doi = "10.1103/PRXQuantum.3.010324",
    journal = "PRX Quantum",
    volume = "3",
    number = "1",
    pages = "010324",
    year = "2022"
}