gen_alg_xxz

Implementation of genetic algorithms to optimize transmission fidelity in quantum spin chains described by XXZ hamiltonians.

Physical Description

We consider spin chains described by XXZ Hamiltonians:

$$ H\ = \sum _{i=1}^{N} J_i \left( \sigma _{i}^{x} \sigma _{i+1}^{x} +\sigma _{i}^{y} \sigma _{i+1}^{y} + \Delta \sigma _{i}^{z} \sigma _{i+1}^{z}\right) $$

with n being the number of elements in the chain. Our goal is to implement genetic algorithms in order to find optimal values for the coupling constants $J_i$. In this case, optimal values mean values that maximize the fidelity when a quantum state is being transmitted through the chain.

Since reflection symmetry is a neccessary condition to obtain perfect transmission, only half of the coupling values are calculated. For example, if the chain has 21 elements, there will be 20 coupling constants $J_i$ and the algorithm will maximize for 10 variables.

To find a detailed explanation of the physical problem, check [1] or [2].

Implementation

These programs use PyGAD library [3] to implement genetic algorithms. The coupling constants are considered as genes and the transmission probability is used to build the fitness function.

Contents

• exp_gen.py: Script to generate and run genetic algorithms experiments. Takes the number of couplings and a directory name to save results as arguments. It generates a configuration file to run the algorithm and saves it along the results and scripts in the specified directory.

• average.py: Script containing the implementation of the genetic algorithm. It reads a provided configuration file and runs the experiment as many times as it is specified in it. It saves the solutions and fitness evolution history for each sample inside the directory listed in the configuration file. It also saves a table containing dimension, fidelity, generations and CPU time for each sample.

• gmod.py: module containing genetic algorithm related functions such as mutations, fitness functions, generation of genespaces, etc.

• ga_graphs.py: module containing different plotting functions to analyze obtained results.

• example.ipynb: Notebook with sample commands and a brief description of how to implement the scripts listed above.

References

[1] - G. M. Nikolopoulos and I. Jex, Quantum State Transfer and Network Engineering. Berlin Springer, 2016

[2] - X.M. Zhang, Z.W. Cui, X. Wang, and M.H. Yung, “Automatic spin-chain learning to explore the quantum speed limit”

[3] - Ahmed Fawzy Gad, "PyGAD: An Intuitive Genetic Algorithm Python Library". Documentation available at: https://pygad.readthedocs.io/en/latest/pygad.html