Pre-release
This release is a pre-release and may not be stable for production use.
Tesseract is a Most Likely Error decoder designed for Low Density Parity Check (LDPC) quantum error-correcting codes. It applies pruning heuristics and manifold orientation techniques during a search over the error subsets to identify the most likely error configuration consistent with the observed syndrome. Tesseract achieves significant speed improvements over traditional integer programming-based decoders while maintaining comparable accuracy at moderate physical error rates.
We tested the Tesseract decoder for:
- Surface codes
- Color codes
- Bivariate-bicycle codes
- Transversal CNOT protocols for surface codes
Features
- A* search: deploys A* search while running a Dijkstra algorithm with early stop for high performance.
- Stim and DEM Support: processes Stim circuit files and Detector Error Model (DEM) files with arbitrary error models. Zero-probability error instructions are automatically removed when a DEM is loaded.
- Parallel Decoding: uses multithreading to accelerate the decoding process, making it suitable for large-scale simulations.
- Efficient Beam Search: implements a beam search
algorithm to minimize decoding cost and enhance efficiency.
Sampling and Shot Range Processing: supports sampling shots from circuits. When a detection
error model is provided without an accompanying circuit, Tesseract requires detection events from
files using
--in. The decoder can also process specific shot ranges for flexible experiment setups. - Detailed Statistics: provides comprehensive statistics output, including shot counts, error counts, and processing times.
- Heuristics: includes flexible heuristic options:
--beam,--det-penalty,--beam-climbing,--no-revisit-dets,--at-most-two-errors-per-detector, and--pqlimitto improve performance while maintaining a low logical error rate. To learn more about these options, use./bazel-bin/src/tesseract --help - Visualization tool: open the viz directory in your browser to view decoding results. See viz/README.md for instructions on generating the visualization JSON.
Installation
Tesseract relies on the following external libraries:
- argparse: For command-line argument parsing.
- nlohmann/json: For JSON handling (used for statistics output).
- Stim: For quantum circuit simulation and error model handling.
Build Instructions
Tesseract uses Bazel as its build system. To build the decoder:
bazel build src:all
Running Tests
Unit tests are executed with Bazel. Run the quick test suite using:
bazel test //src:all
By default the tests use reduced parameters and finish in under 30 seconds. To run a more exhaustive suite with additional shots and larger distances, set:
TESSERACT_LONG_TESTS=1 bazel test //src:all
Usage
The file tesseract_main.cc provides the main entry point for Tesseract Decoder. It can decode
error events from Stim circuits, DEM files, and pre-existing detection event files.
Basic Usage:
./tesseract --circuit CIRCUIT_FILE.stim --sample-num-shots N --print-stats
To decode pre-generated detection events, provide the input file using
--in SHOTS_FILE --in-format FORMAT.
Example with Advanced Options:
./tesseract \
--pqlimit 1000000 \
--at-most-two-errors-per-detector \
--det-order-seed 232852747 \
--circuit circuit_file.stim \
--sample-seed 232856747 \
--sample-num-shots 10000 \
--threads 32 \
--print-stats \
--beam 23 \
--num-det-orders 1 \
--shot-range-begin 582 \
--shot-range-end 583
Example Usage
Sampling Shots from a Circuit:
./tesseract --circuit surface_code.stim --sample-num-shots 1000 --out predictions.01 --out-format 01
Using a Detection Event File:
./tesseract --in events.01 --in-format 01 --dem surface_code.dem --out decoded.txt
Using a Detection Event File and Observable Flips:
./tesseract --in events.01 --in-format 01 --obs_in obs.01 --obs-in-format 01 --dem surface_code.dem --out decoded.txt
Tesseract supports reading and writing from all of Stim's standard output formats.
Performance Optimization
Here are some tips for improving performance:
- Parallelism over shots: increase
--threadsto leverage multicore processors for faster decoding. - Beam Search: use
--beamto control the trade-off between accuracy and speed. Smaller beam sizes result in faster decoding but potentially lower accuracy. - Beam Climbing: enable
--beam-climbingfor enhanced cost-based decoding. - At most two errors per detector: enable
--at-most-two-errors-per-detectorto improve performance. - Priority Queue limit: use
--pqlimitto limit the size of the priority queue.
Output Formats
- Observable flips output: predictions of logical errors.
- DEM usage frequency output: if
--dem-outis specified, outputs estimated error frequencies. - Statistics output: includes number of shots, errors, low confidence shots, and processing time.
Python Interface
This repository contains the C++ implementation of the Tesseract quantum error correction decoder, along with a Python wrapper. The Python wrapper/interface exposes the decoding algorithms and helper utilities, allowing Python users to leverage this high-performance decoding algorithm.
The following example demonstrates how to create and use the Tesseract decoder using the Python interface.
import tesseract_decoder.tesseract as tesseract
import stim
# 1. Define a detector error model (DEM)
dem = stim.DetectorErrorModel("""
error(0.1) D0 D1
error(0.2) D1 D2 L0
detector(0, 0, 0) D0
detector(1, 0, 0) D1
detector(2, 0, 0) D2
""")
# 2. Create the decoder configuration
config = tesseract.TesseractConfig(dem=dem, det_beam=50)
# 3. Configure and create a decoder instance
decoder = tesseract.TesseractDecoder(config)
# 4. Simulate detection events and decode it
detections = [1, 2]
flipped_observables = decoder.decode(detections)
print(f"Detections: {detections}")
print(f"Flipped observables: {flipped_observables}")
For full documentation and detailed examples of the Python interface, please refer to the docs.
Help
- Do you have a feature request or want to report a bug? Open an issue on GitHub to report it!
- Do you have a code contribution? Read our contribution guidelines, then open a pull request!
We are committed to providing a friendly, safe, and welcoming environment for all. Please read and respect our Code of Conduct.
Citation
When publishing articles or otherwise writing about Tesseract Decoder, please cite the following:
@misc{beni2025tesseractdecoder,
title={Tesseract: A Search-Based Decoder for Quantum Error Correction},
author = {Aghababaie Beni, Laleh and Higgott, Oscar and Shutty, Noah},
year={2025},
eprint={2503.10988},
archivePrefix={arXiv},
primaryClass={quant-ph},
doi = {10.48550/arXiv.2503.10988},
url={https://arxiv.org/abs/2503.10988},
}
Contact
For any questions or concerns not addressed here, please email quantum-oss-maintainers@google.com.
Disclaimer
Tesseract Decoder is not an officially supported Google product. This project is not eligible for the Google Open Source Software Vulnerability Rewards Program.
Copyright 2025 Google LLC.
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