Morse Potential on a Quantum Computer

This code is designed to run the Variational Quantum Eigensolver (VQE) algorithm from IBM's Quantum Information Software Kit (QISKit) on Hamiltonians represented as text files. This code was written while participating the in the spring 2020 Science Undergraduate Laboratory Internships (SULI) program at Brookhaven National Laboratory.

Directory

• mathematica_nbs: Contains all Mathematica notebooks used to create text file representation of Hamiltonians for each basis.
• out_puts: Contains all of the outputs generated from running VQE on the Morse potential with 4 qubits in each basis. _data.pkl files contain serialized raw data from the simulaiton and can be used to do further analysis on simulation results. _output.txt outlines all of the parameters and results in an easily readable table format.
• py_files: Contains two python scripts. VQE_class.py is a class that can be used to run VQE, plot the results, and save results. morse_energy_levels.py is a script that plots the first four Morse potential Hamiltonians and the first four bound states.
• tutorials: Contains a jupyter notebook and necessary Hamiltonian text files for giving an introdcution to the variatonal method and going through a VQE run step by step for the harmonic and anharmonic oscillator.
• text_file_hamiltonians: Contains all text file representation Hamiltonians used for VQE. This is so one can try running VQE on their own without having a Mathematica liscense.

Before getting started

I recommend creating a conda environment to do all of you work in since the code running without errors is fairly version dependent when using QISKit.

1. Install Anaconda (version: 4.8.3)
2. Open terminal, run: conda create -n <environment_name> (replace environment_name with whatever you want to name your environment).
3. Activate Environment: conda activate <environment_name>
4. Install QISKit: pip install qiskit==0.16.2
5. When finished make sure to deactive the environment: conda deactivate <environment_name>

Hamiltonian file name convention

Currently the code gets the state and basis from the file name of the text file representation of the Hamiltonian. The convention is is follows: Potential_basis_energystate_sizexsize.txt Also, after running VQE on many Hamiltonians, we found that the classical optimizers have a hard time when the energy is zero or close to it. A way around this is to hold off on adding a constant that would result in the energy becoming zero until after the optimizers are done. To impliment this, add nonzero anywhere in the file name after the energy state, e.g. Potential_basis_energystate_nonzero_sizexsize.txt or Potential_basis_energystate_sizexsize_nonzero.txt

• Potential: Name of potential the VQE is being ran on (e.g. Morse or AnharmonicOscillator)
• Basis: How the Hamiltonian is constructed
  • Position pos
  • Oscillator osc
  • Finite Difference finite
• The energy state is representented as , for the i th energy state
  • e.g. Ground state E0
  • First excited state E1
• Size: Size of the Hamiltonian matrix (determined by the number of qubits used)
  • N qubits matrix

For example, if you were running the Morse potential in the position basis, calculating the ground state, and used $4$ qubits, the file name would be Morse_pos_E0_16x16.txt

Prerequisites

Make sure you either have the Hamiltonian text files you plan to use in the same directory as this script or input the full path into the file_path key in your param dictionary.

If planning to use IBM's Q Experience API: make a python script titled my_secrets.py and define a string with your unique IBMQ API token as its value. Ex: pw = 'your_API_key'

The main packages used are outlined below. Note that QISKit is very new and the developers release new versions often and a lot of methods and functions get depricated regularly. I will not be updating this code to work with any newer versions of QISKit. I outline the versions of QISKit that work with this code. You can install specific versions of QISKit through pip with the following command: pip insall qiskit==0.16.2

System information: Python 3.8.0 (default, Nov 6 2019, 21:49:08) [GCC 7.3.0] Conda Version: 4.8.3

os
sys
time
numpy
pickle
pandas
seaborn
datetime
tabulate
matplotlib

QISKit Version Information

Qiskit Software	Version
Qiskit	0.16.2
Terra	0.12.0
Aer	0.4.1
Ignis	0.2.0
Aqua	0.6.5
IBM Q Provider	0.5.0

Example

Due to the large number of parameters VQE has, I recommed creating a parameter dictionary to organize all of them in an easily readable way. Below is a snippet of code that will run VQE on a Hamiltonian of your choice, save all of the raw data & general output, and generate three plots (energy convergence, best optimizer convergence, and statevectors for each optimizer).

params = {
	'file_path':fr'Morse_pos/Morse_pos_E0_16x16.txt',
	'init_state_name':Zero,
	'vf_name':RY,
	'depth':1,
	'shots':1,
	'simulator': 'statevector_simulator'
}

v_q_e = RunVQE(params)					# Runs VQE, prints parameters & results
v_q_e.save_data_to_pkl(f'{v_q_e.file_name}_data.pkl')	#Saves raw data from simulation
v_q_e.save_output(f'{v_q_e.file_name}_output.txt')	#Saves tabular output
v_q_e.plt_energy_convergence()
v_q_e.plt_opt_convergence()
v_q_e.plt_state_vector()

Authors

• Joshua Apanavicius

Acknowledgments

• My mentor for this project, Michael D. McGuigan
• The United States Department of Energy, for funding the SULI program
• Brookhaven National Laboratory, for hosting my stay and allowing me to participate in this project

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