Surface Code Simulation (Qiskit & Stim)

This project implements and simulates the surface code, one of the leading quantum error-correcting codes, using two frameworks:

• Qiskit for circuit-based simulations
• Stim for fast stabilizer circuit sampling

It explores how stabilizer measurements detect Pauli errors (X, Y, Z) and how noise affects logical qubits.

Project Structure

Qiskit/
├── Modular_Simple_Circuit.ipynb        # Modular Surface Code using Qiskit
├── Simple Model Circuit 4 qubits.ipynb # Example with 4-qubit entangled state
├── SurfaceCode.py                      # Qiskit-based surface code implementation

STIM/
├── Modular_Simple_Circuit_STIM.ipynb   # Modular Surface Code using Stim
├── SurfaceCodeSTIM.py                  # Stim-based surface code simulator

README.md                                # Project documentation

Features

• Surface code construction for arbitrary distance (d).
• Stabilizer measurement circuits (X and Z stabilizers) on a planar 2D lattice.
• Noise models: Pauli depolarizing noise ((X, Y, Z) errors with probability (p)).
• Visualization tools:
  • Single-shot stabilizer measurement timelines.
  • Histograms of multi-shot syndrome distributions.

Example: Syndrome Measurement

• X stabilizers detect Z and Y errors.
• Z stabilizers detect X and Y errors.
• Y errors flip both stabilizer types.

A minimal-weight perfect matching (MWPM) decoder can then be applied to infer the most likely error configuration.

Background

The surface code encodes logical qubits in a 2D grid of physical qubits with local stabilizer checks. A distance-(d) code can detect and correct up to (\left\lfloor \frac{d-1}{2} \right\rfloor) errors.

Next Steps

• Implement a decoder (e.g., Edmonds’ Minimum-Weight Perfect Matching).
• Explore logical error rates as a function of noise probability (p).
• Extend to rotated surface codes or other topological codes.