Solving quantum state diffusion (QSD) numerically.

The script quantum_state_diffusion.py can be used to run QSD simulations. I am using a (slightly) modified version of a package called sdeint. The only modification I made is to normalize the trajectories for numerical stability.

My version can be found on https://github.com/tabakg/sdeint

There are two notebooks currently, one for the Kerr system and the second for the absorptive bi-stability. Please compare the results to those obtained using quantum jump trajectories (found on this repo).

Running

You have several options for running the simulation, including container-based and local environments:

• Docker
• Singularity
• Local Environment
• Cluster (SLURM example)

Depending on your familiarity with containers, the first two are recommended to handle software dependencies. Complete instructions are included below.

Docker

The development environment is Dockerized, meaning that you can run the simulation with a Docker image. First, you need to install Docker. The base command to see help for how to run:

  docker run tabakg/quantum_state_diffusion --help

will show you the following (after a message about the font cache):

usage: make_quantum_trajectory.py [-h] [--seed SEED] [--ntraj NTRAJ]
	                          [--duration DURATION] [--delta_t DELTAT]
	                          [--Nfock_a NFOCKA] [--Nfock_j NFOCKJ]
	                          [--downsample DOWNSAMPLE] [--quiet]
	                          [--output_dir OUTDIR] [--save2pkl]
	                          [--save2mat]

generating trajectories using quantum state diffusion

optional arguments:
  -h, --help            show this help message and exit
  --seed SEED           Seed to set for the simulation.
  --ntraj NTRAJ         number of trajectories, should be kept at 1 if run via
	                slurm
  --duration DURATION   Duration in ()
  --delta_t DELTAT      Parameter delta_t
  --Nfock_a NFOCKA      Parameter N_focka
  --Nfock_j NFOCKJ      Parameter N_fockj
  --downsample DOWNSAMPLE
	                How much to downsample results
  --quiet               Turn off logging (debug and info)
  --output_dir OUTDIR   Output folder. If not defined, will use PWD.
  --save2pkl            Save pickle file to --output_dir
  --save2mat            Save .mat file to --output_dir

Run and save to local machine

Note that the --quiet option can be added to silence printing. By default, no data is saved. To save, you will need to 1) specify the output directory to the /data folder in the container using the output_dir argument and 2) map some directory on your local machine to this /data folder. We can do that like this:

       # on your local machine, let's say we want to save to Desktop
       docker run -v /home/vanessa/Desktop:/data \
                     tabakg/quantum_state_diffusion --output_dir /data --save2pkl

The above will produce the following output:

INFO:root:Parameter Ntraj set to 1
INFO:root:Parameter Nfock_j set to 2
INFO:root:Parameter duration set to 10
INFO:root:Parameter delta_t set to 0.002
INFO:root:Parameter downsample set to 100
INFO:root:Parameter Nfock_a set to 50
INFO:root:Parameter seed set to 1
INFO:root:Downsample set to 100
INFO:root:Regime is set to absorptive_bistable
Run time:   2.1634318828582764  seconds.
INFO:root:Saving pickle file...
INFO:root:Saving result to /data/QSD_absorptive_bistable_1-1-0.002-50-2-10.pkl
INFO:root:Data saved to pickle file /data/QSD_absorptive_bistable_1-1-0.002-50-2-10

The final output will be in the mapped folder - in the example above, this would be my Desktop at /home/vanessa/Desktop/QSD_absorptive_bistable*.pkl

Run inside container

You may want to inspect the data using the same environment it was generated from, in which case you would want to shell into the container. To do this, you can run:

  docker run -it --entrypoint=/bin/bash tabakg/quantum_state_diffusion

if you type ls you will see that we are sitting in the /code directory that contains the core python files. This means that we can run the analysis equivalently:

/code# python make_quantum_trajectory.py --output_dir /data --save2pkl
INFO:root:Parameter downsample set to 100
INFO:root:Parameter duration set to 10
INFO:root:Parameter seed set to 1
INFO:root:Parameter Nfock_j set to 2
INFO:root:Parameter Nfock_a set to 50
INFO:root:Parameter delta_t set to 0.002
INFO:root:Parameter Ntraj set to 1
INFO:root:Downsample set to 100
INFO:root:Regime is set to absorptive_bistable
Run time:   2.183995485305786  seconds.
INFO:root:Saving pickle file...
INFO:root:Saving result to /data/QSD_absorptive_bistable_1-1-0.002-50-2-10.pkl
INFO:root:Data saved to pickle file /data/QSD_absorptive_bistable_1-1-0.002-50-2-10

and the data is inside the container with us! Great.

root@4420ae9e385d:/code# ls /data
QSD_absorptive_bistable_1-1-0.002-50-2-10.pkl

Customize the Docker image

If you don't want to use the image from Docker Hub (for example, if you want to make changes first) you can also build the image locally. You can build the image by doing the following:

  git clone https://www.github.com/tabakg/quantum_state_diffusion
  cd quantum_state_diffusion
  docker build -t tabakg/quantum_state_diffusion .

Note the . at the end of the command to specify the present working directory.

Singularity

Singularity is a container that is HPC friendly, meaning that it can be run on a cluster environment. The container itself, a file that sits on your computer, can be dropped into a folder on your cluster, and run like a script! We have provided a Singularity file that can bootstrap the Docker image to build the image.

1. Install Singularity

Instructions can be found on the singularity site.

2. Bootstrap the image

sudo singularity create --size 4000 qsd.img
sudo singularity bootstrap qsd.img Singularity

3. Run commands

How to access the python executable?

  ./qsd.img --help
usage: make_quantum_trajectory.py [-h] [--seed SEED] [--ntraj NTRAJ]
	                          [--duration DURATION] [--delta_t DELTAT]
	                          [--Nfock_a NFOCKA] [--Nfock_j NFOCKJ]
	                          [--downsample DOWNSAMPLE] [--quiet]
	                          [--output_dir OUTDIR] [--save2pkl]
	                          [--save2mat]

generating trajectories using quantum state diffusion

optional arguments:
  -h, --help            show this help message and exit
  --seed SEED           Seed to set for the simulation.
  --ntraj NTRAJ         number of trajectories, should be kept at 1 if run via
	                slurm
  --duration DURATION   Duration in ()
  --delta_t DELTAT      Parameter delta_t
  --Nfock_a NFOCKA      Parameter N_focka
  --Nfock_j NFOCKJ      Parameter N_fockj
  --downsample DOWNSAMPLE
	                How much to downsample results
  --quiet               Turn off logging (debug and info)
  --output_dir OUTDIR   Output folder. If not defined, will use PWD.
  --save2pkl            Save pickle file to --output_dir
  --save2mat            Save .mat file to --output_dir

You might again want to map a folder for the data output

  singularity run --bind /home/vanessa/Desktop:/data/ qsd.img --output_dir /data --save2pkl

And you again might want to interactive work in the container

  sudo singularity shell --writable qsd.img
  cd /code
  ls

Cluster Usage

Running on a local machine is fine, but it will not scale well if you want to run thousands of times. Toward this aim, we have provided simple SLURM submission scripts to help! They are optimized for the sherlock cluster at Stanford (which has Singularity installed), however you can easily modify the submission command to run natively on a cluster without it (more detail below). For both, you can use the scripts in slurm. You will want to do the following:

1. Build the Singularity image

Using the steps above, build the Singularity image, and use some form of FTP to transfer the image to your cluster. We must do this because it requires sudo to build and bootstrap the image, but not to run it (you do not have sudo permission on a cluster).

2. Create a folder to work from

In your $HOME folder in your cluster environment, you likely want to keep a folder to put your image, and organize input and output files:

  cd $HOME
  mkdir -p SCRIPTS/SINGULARITY/QSD
  cd SCRIPTS/SINGULARITY/QSD # transfer qsd.img here

And then write run.py into a file in that location. In a nutshell, this script is going to create local directories for jobs, output, and error files (.job,.out,.err), and then iterate through a variable in the simulation (the seed) and submit a job for each on our partition of choice. The variables you should / might be interested in editing are in the header:

Data Output

Each pickle file contains the simulation result, along with the dictionary of analysis parameters. For example, here we are loading a pickle result file:

import pickle
mdict = pickle.load(open('QSD_absorptive_bistable_1-1-0.002-50-2-10.pkl','rb'))

# What result keys are available?
result.keys()
dict_keys(['Nfock_a', 'Ntraj', 'observable_str', 'Nfock_j', 'times', 'psis', 'downsample',   
           'seeds', 'expects', 'delta_t', 'seed', 'duration', 'observable_latex'

With this data, you can do interactive plotting and further analysis, examples which will be provided in this repo (under development).

Local Installation:

Installation requires Python 3.

In addition to standard libraries (numpy, sympy, scipy, pickle)

In addition to the modified version of sdeint found on https://github.com/tabakg/sdeint (mentioned above), please install QNET (https://pypi.python.org/pypi/QNET). QNET is on pip, and can be installed simply with:

pip install QNET.

I am also using a package called multiprocess, which can be installed with

pip install multiprocess