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Tutorial: Decoding Quantum Errors on the Steane code with Belief Propagation & Catalyst #1371

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@beitom beitom commented May 14, 2025

Title: Decoding Quantum Errors on the Steane code with Belief Propagation & Catalyst

Summary:
This tutorial walks you through a simplified error correction cycle using the Steane $[[7,1,3]]$
code. You’ll encode a logical qubit, introduce noise, extract syndromes, and apply decoding using
two different strategies: a simple lookup table and a belief propagation (BP) decoder. Both decoders
are implemented in JAX and JIT-compiled by Catalyst, allowing everything to run inside a single
@qml.qjit circuit.

Relevant references:

Possible Drawbacks:
The tutorial uses a simplified noise model (code capacity) where errors occur only once. Real-world quantum computers have errors at every step (circuit-level noise), which creates a much more complex decoding challenge involving errors in space and time.

Related GitHub Issues:
N/A


If you are writing a demonstration, please answer these questions to facilitate the marketing process.

GOALS — Why are we working on this now?

I work on fault tolerant compilation of quantum circuits which involves making classical decoding algorithms run alongside quantum circuit with measurements and feedforward operations. Catalyst is a great new technology to enable these kinds of high performance hybrid quantum-classical workflows essential for quantum error correction.

AUDIENCE — Who is this for?

  • Quantum computing researchers interested in QEC.
  • Developers working with Pennylane and Catalyst on hybrid workflows for QEC.
  • Educators teaching stabilizer codes or decoding techniques.

KEYWORDS — What words should be included in the marketing post?

quantum error correction, css code, hybrid quantum-classical, belief propagation decoding, JAX, Catalyst

  • Which of the following types of documentation is most similar to your file?
    (more details here note this requires a Xanadu email to view)
  • Tutorial
  • Demo
  • How-to

Notes:

suggested thumbail is to make a graphic of the Steane code in it's usual triangle layout
image

The hero image should have some theme of quantum/classical QEC circuits my idea is roughly this where S is the syndrome and R is the recovery operator:

image

[sc-93094]

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@daniela-angulo daniela-angulo self-assigned this Jun 17, 2025
Comment on lines 1 to 8
{
"title": "Decoding Quantum Errors on the Steane code with Belief Propagation & Catalyst",
"authors": [
{
"username": "tomginsberg"
}
],
"dateOfPublication": "2025-05-14T00:00:00+00:00",
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This and any files in demonstrations/ directory can be deleted.

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@alvaro-at-xanadu alvaro-at-xanadu left a comment

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Looks great! Please update metadata date before merging

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5 participants