Quantum Solution to the Byzantine Agreement Problem in Qiskit

Description

In the seminal article by Lamport, Shostak and Marshal, it was proven that no classical solution with less than 3⋅𝑚+1 generals can face 𝑚 traitors. A quantum solution for 3 generals using qutrits is described here and can be done with qubits entangled in such a way that they emulate qutrits as shown here and here.

In this project, the cases of 3 and 4 generals are solved by algorithms based respectively on entangled qutrits and entangled ququatrits. These qu-n-its are emulated by adequately entangled qubits. I tested successfully these algorithm for qutrits in Qiskit on qasm_simulator and FakeCasablanca or other mock backgrounds. For ququatrits, the algorithm passes the test on qasm simulator, or on a modified mock background (FakeSydney with gate errors and read out errors all set to their observed average across qubits).

This project seems quite close to completion for the mentees, who may be frustrated. It is therefore probably preferable that I play myself the role of the mentee if I find a mentor interested in this issue.

Deliverables

a notebook (nearly completed)
further testing the 4-general solution on noise models
if possible, hardware testing for the 3-general solution
an article submitted to qiskit Medium, or another type of publication

Mentors details

Call for a mentor (or co-author of the project) who could review the notebook, see if there are some flaws, accompany me in the verification on hardware, and help me with the publication. I will be the mentee, but, why not, the mentor. The main point is to form a team interested by the quantum solutions of the Byzantine agreement problem. Those who are interested can DM me on Slack @PierreDC. I shall transmit the current state of the notebook which includes a more complete description of the project in introduction.

Number of mentees

Type of mentees

(and of mentor)

Interested by the Byzantine agreement problem and its quantum solutions
Can be useful: some knowledge in areas such as finance and bitcoins, probabilities, quantum cryptography, game theory, quantum games and paradoxes

qiskit-advocate / qamp-spring-22