ibmq_green_dvmc

Warning: This code is untested for Windows and MacOS. Works on linux Ubuntu.

Table of Contents

• Installation
• Description
• How it works
• Execution
• Examples
• Todo

Installation

This is a Python code. Use the latest version of language as of 29/07/2023 to avoid issues. To run this code, you will need to install the following packages for your Python. The links to their documentation is also provided :

• qiskit--> (https://qiskit.org/documentation/getting_started.html) VERSION: 0.43.2
• qiskit-nature--> (https://qiskit.org/ecosystem/nature/getting_started.html) VERSION: 0.6.2
• qiskit-aer-->(https://qiskit.org/ecosystem/aer/getting_started.html) VERSION: 0.12.1
• qiskit-ibm-runtime--> (https://qiskit.org/ecosystem/ibm-runtime/getting_started.html) VERSION: 0.11.2
• qiskit-ibm-provider--> (pip install qiskit-ibm-provider==0.6.1) VERSION: 0.6.1
• matplotlib--> (https://matplotlib.org/stable/users/getting_started/index.html#installation-quick-start)
• numpy--> (https://numpy.org/install/)
• mpire--> (https://sybrenjansen.github.io/mpire/v2.3.0/install.html)
• mapomatic--> (https://github.com/Qiskit-Partners/mapomatic)
• [OPTIONAL] pyqcm--> (https://qcm-wed.readthedocs.io/en/latest/intro.html#installation)

Note that the "qcm" package is not manditory as its only purpose is to benchmark the calculations using the quantum computer.

Description

This code is meant to calculate the Green Function for a specified system of low amount of sites. Instead of calculating it using conventional binary based computers, we simulate the calculation on a quantum computer using the qiskit package.

The code itself is accompanied by a few supplementary benchmarks codes. These benchmark codes come in two types : benchmarks that use a custom second quantization base implementation, and benchmarks that use the "qcm" package. The usage of those benchmarks is explained in the following section.

How it works

The primary use of this code is to calculate the Green Function. I will walktrough you in calculating it using the codes in quantum_computer_codes/.

All the files located in quantum_computer_codes/ are useful to the calculation of the Green Function for any systems. Here is the uses of each individual files in this folder.

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• The parameters.py file is where you can modify the parameters and variables to be used by all the files in the folder. It is also where you need to modify your lattice structures and circuit configurations if you are opting for a customized model. Specifications on the inner workings of the lattice and circuit objects are located in the "qiskit" package documentation. As for the qcm lattice, its usage is specified in its own documentation. One thing to note though it the HOPPING MATRIX. If the code detects it cannot create a grid lattice with the specified number of sites, you need to change manually the hopping matrix. Also, if you want to change the output folders, these can be modified at the very end of parameters.py. However, I would recommend to not touch this portion to avoid any problems.
• The generate.py is meant to generate the specified matrices, print them in the CMD and save them as .npy files in output/.
• The graph.py is to make a graph with the generated matrices. The code will use the right set of matrices depending if you are generating a graph from the quantum computer matrices or the fock benchmark matrices. The spectrum is outputted as a pdf in the same folder as parameter.py, and its file name corresponds to which matrices were used (ibmq or fock). This code also outputs a local_dos.dat file in output/.
• The hamiltonian_circuit.py contains the hidden code to generate automatically grid shapped lattices for all implementations of the green function calculation (qiskit, qcm and fock).
• The mapping.py contains the code that finds the best possible qubits for the calculation. This code was provided by a collegue. It doesn't seem to work with some circuits.

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• The qcm_benchmark.py, similarly to graph.py, will generate a graph of the Green Function using the "qcm" package. Said graph will be called qcm_spectrum.pdf. The file also generates a local_dos_qcm.dat file in output/.

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• The fock_benchmark, similarly to graph.py, will generate a graph of the Green Function using my implementation of the second quantization base. Said graph will be called fock_spectrum.pdf. The file also generates a local_dos_fock.dat file in output/.

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• The combined_graphs.py file, using the two or three .dat files in the output/ directory, generates a combined graph of the Green Function calculated by 3 methods (ibmq,fock and qcm) or only 2 methods (ibmq and fock). This is meant to directly compare these methods.

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• The excitationNsites.def, located in excitation_files/, is the file containing all the excitation types of the system. If this file is to be changed, it needs to respect the exact formatting of the current files.

Execution

The parameters.py can be copied from quantum_computer_codes/ and pasted anywhere in the operating system. Then, change the parameters, lattices and the circuit in the file to your needs. If you want a custom excitation.def file to be used, in the same directory as your parameter.py file, have the excitation.def you want. Then, to run any of the codes, execute this line in the command line (CMD): $ python3 path/to/code/thecode.py. For the following procedure, we assume that you are located within the quantum_computer_codes directory, hence there is no path/to/code/.

Running the quantum computer simulation

Run these the first time:

$ python3 generate.py
$ python3 graph.py

Your ibmq_spectrum.pdf is stored in the same folder as parameters.py. As long as graph.py is provided matrices, the code can work idependantly or, in other words, without running generate.py before.

Running the qcm benchmark

Run this:

$ python3 qcm_benchmark.py

Your qcm_spectrum.pdf is stored in the same folder as parameters.py. Note that in the event the the ground_state is located in a block where the total spin is not of 0, you will need to modify this code to target the proper block for the calculation. However, this occurence is highly unlikely.

Running the fock benchmark

Run this:

$ python3 fock_benchmark.py

Your fock_spectrum.pdf is stored in the same folder as parameters.py.

Combining the graphs

Run this:

$ combined_graphs.py

Your combined_spectrum.pdf is stored in the same folder as parameters.py.

Examples

In the directory quantum_computer_codes/examples, there are some directories containing basic examples that show how to run the code. Refer to the README in this directory.

TODO

• Debugging.