An Optimized Implementation of Quantum Information Set Decoding on Scalable Quantum Resources

Supplementary code

This repository is related to the paper with the same title in:

It contains the code necessary to reproduce the circuits specified in the text and run simulations using the Qibo library available in: https://github.com/qiboteam/qibo

The code has been limited to a maximum of 29 qubits in order for them to be run on most classical hardware.

This reposotory contains:

• functions.py: set of functions and classes used for the creation of the quantum circuits for quantum ISD, amplitude amplification and instance generation including Lee-Brickell modifications.

• main.py: solving an instance of a linear code using quantum Information Set Decoding using quantum simultion software.

• hybrid.sage: using a hybrid classical-quantum approach to solve large instances with limited quantum resources.

How to run the code:

main.py

• --n (int) : code length, number of columns of the parity check matrix.
• --k (int) : code dimension, parity check matrix consists of n-k rows.
• --target (int) : target weight for the solution.
• --num_sol (int) : number of solutions of the instance. Leave blank if not known.
• --execute : flag to execute the simulation of the quantum circuit.
• --iterative : flag to force the use of the iterative method even when the number of solutions is known.
• --verbose : flag to output superposition and oracle sanity checks.
• --circuit : flag to output a .qasm file with the gates required to solve the quantum ISD instance.
• --it (int) : number of amplitude amplification iterations for the circuit printed.
• --summary : flag to output the number of gates and depth of the quantum circuit.
• --lee_brickell (int) : number of assumed weight in non chosen columns. If 0 run standard ISD.

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hybrid.sage

• --n (int) : code length, number of columns of the parity check matrix.
• --k (int) : code dimension, parity check matrix consists of n-k rows.
• --w (int) : error weight of the syndrome decoding instance.
• --alpha (int) : optimization parameter of hybrid prange, zeros to be guessed.
• --beta (int) : optimization parameter of punctured hybrid, omitted rows.
• --p (int) : optimization parameter of punctured hybrid, weight on omitted part.