Two mini-projects have been implemented: a “Quantum Calculator” and a “Five-Qubit Code under Random Pauli Error.”

The first project consists of a quantum extension of the standard Draper’s adder, a method that allows adding an integer to a quantum register, effectively shifting the computational basis. Here, instead of adding an integer, a routine was developed to add two quantum registers directly. This required a combination of quantum Fourier transforms and their inverses.

The second project builds the five-qubit error-correcting code, the smallest perfect code capable correcting any single-qubit error. Random noise is applied to each qubit, and the code performs conditional recovery to preserve quantum information. A final graph shows that as the probability of an error increases, the code’s ability to correct all errors decreases exponentially.

Project 1: https://github.com/FilBalza/Quantum-Calculator
Project 2: https://github.com/FilBalza/Five-qubits-with-Pauli-errors