Quantum Error Correction

Computational studies of quantum error correction using Python and Qiskit.

This repository currently contains an implementation and analysis of the five-qubit [[5,1,3]] stabilizer code.

Five-Qubit Code

Notebook: five-qubit-code/five_qubit_code.ipynb

The notebook:

• derives syndromes for all 15 single-qubit Pauli errors;
• constructs the stabilizer group;
• verifies the exact code distance, d = 3, by exhaustive search over five-qubit Pauli operators;
• shows that the code saturates the quantum Hamming bound;
• prepares and verifies logical code states;
• constructs a four-ancilla syndrome-extraction circuit;
• verifies recovery of all 15 weight-one Pauli errors using statevector simulation;
• compares the ideal syndrome for an X_1 error with results from a recorded IBM Quantum hardware run.

Requirements

Tested with:

• Python 3.13.7
• Qiskit 2.2.3
• qiskit-ibm-runtime 0.43.1
• NumPy 2.3.2

Install the required packages with:

python -m pip install -r requirements.txt

The IBM hardware section uses recorded results by default and does not submit a new job. Running a new hardware experiment requires IBM Quantum credentials configured locally.