variational channel fidelity estimation

Source code used for variational quantum fidelity estimation for quantum channels.

Quick start

1. Run generator.py to produce a sample of random channels. By default 1000 channels are generated.
2. Run vqcd_optimization.py n, where n is the index of the channel generated in the previous steps.
3. Run vqcd_all_chan.py, to generate and save the average error in fidelity estimation with respect to rank of the state.
4. Run vqcd_single_chan.py to generate and save the error in fidelity estimation for the lowest error channel. Note to generate the lowest error quantum channel run lowest_error_channel.py, which saves the channel number with lowest error.
5. Run vqcd_plot.py to generate and save the plots.

Description

This repository contains source code for running diagonalization procedure as well as to estimate fidelity (error in fidelity estimation) for 1 and 2 qubit channels.

Code for quantum channels

The main folder contains the following files:

• generate.py for generating random channels. The generated channels are saved in the data subdirectory,

• vqcd_main_funcs.py contains the main subroutines of the diagonalization and fidelity estimation algorithm as follows

  • cost_func cost function evaluation,
  • eig_info inferred eigenvalues generation and
  • trun_output (truncated fidelity bounds estimation) functions.

• vqcd_secondary_funcs.py contains secondary subroutines as follows

  • jamilchoi generates Choi–Jamiołkowski (JC) state of any dimension quantum channel,
  • purity_before_diag gives the purity of the state before diagonalization,
  • maximum_likelihood performs maximum-likelihood to avoid negative eigenvalues.

• vqcd_optimization.py n, where n is the index of the channel generated (if no n provided then the index by default is 0) to run optimization procedure for random quantum channels, by default the optimized angles are saved in data/opt_ang_test subfolder,

• vqcd_all_chan.py for finding the average error in fidelity estimation (by default the channel number set to 1000), by default the average error for each channel are saved in data/fid_plot_data_test subfolder,

• vqcd_single_chan.py for finding the convergence of fidelity with rank of the state for a particular quantum channel, by default the average error for each channel are saved in data/fid_plot_data_test subfolder,

• vqcd_plot.py for plotting the results and contains two subroutines as follows

  • average_fidelity returns plot for average fidelity estimation error for a defined total number of channels,
  • single_chan_fidelity returns plot for a single channel depicting truncated fidelity bound in respect with rank of the JC state. Plots are saved in plot subdirectory

Folder text

This folder is a placeholder for the preprint files.

License

This code can be distributed under the Apache License.

Installation and requirements

Python scripts in this repository have been tested with

• qiskit (0.18.2)
• numpy (1.21.2)
• scipy (1.7.1)

To install the recent version of Qiskit run

!pip install qiskit==0.18.2