Awesome TQEC

A curated list of awesome topological quantum error correction resources.

Table of Contents

• Papers
• Software
• Tutorials and Talks
• Links

Papers

Simulator

• Stim: a fast stabilizer circuit simulator

Lattice Surgery

• Surface code quantum computing by lattice surgery
• Low overhead quantum computation using lattice surgery
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Flexible layout of surface code computations using AutoCCZ states
• Inplace Access to the Surface Code Y Basis - Optimization of logical Y-basis measurement and logical S gate.
• Cleaner magic states with hook injection - Optimization of magic state injection.
• Yoked surface codes - Reduce the overhead by concatenating surface code into parity check codes.
• A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing - Synthesizer for lattice surgery subroutines.

Cluster State

Understand the TQEC structure from the view of cluster state.

• Measurement-based quantum computation with cluster states
• Topological cluster state quantum computing

ZX-Calculus

Understand the TQEC structure from the view of zx-calculus.

• Unifying flavors of fault tolerance with the ZX calculus
• The ZX calculus is a language for surface code lattice surgery

Time-dynamic Circuits

Using time-dynamic circuit without changing the underlying quantum code to achieve better performance/overhead or else.

• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• New circuits and an open source decoder for the color code

Decoder

Minimum-weight Perfect Matching(MWPM)

• Towards practical classical processing for the surface code: Timing analysis
• Sparse Blossom: correcting a million errors per core second with minimum-weight matching - Speedup MWPW by sparse blossom algorithm on decoding graph.
• Fusion Blossom: Fast MWPM Decoders for QEC - Similar idea to Sparse Blossom, speedup MWPM by fusion blossom on decoding graph.
• Optimal complexity correction of correlated errors in the surface code - Enhance MWPM by recursive correlated matching.
• Pipelined correlated minimum weight perfect matching of the surface code - Correlated matching with pipelined method.

Union-find(UF)

• Almost-linear time decoding algorithm for topological codes
• Fault-tolerant weighted union-find decoding on the toric code - Weighted union-find decoder.

Tensor Network(TN)

• Efficient algorithms for maximum likelihood decoding in the surface code - MLD for surface code under code-capacity noise.
• Tensor Network Decoding Beyond 2D - MLD for surface code under circuit-level noise.

Neural Network(NN)

• Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network

Parallel Window

• Scalable surface code decoders with parallelization in time
• Modular decoding: parallelizable real-time decoding for quantum computers
• Parallel window decoding enables scalable fault tolerant quantum computation

Belief Propagation

• Improved decoding of circuit noise and fragile boundaries of tailored surface codes - Two-stage decoding combining belief propagation and MWPM/UF.

Experiment

• Suppressing quantum errors by scaling a surface code logical qubit - Suppression of logical error when scaling surface code from distance 3 to 5.

Software

Simulator

• Stim - A fast stabilizer circuit library.

• Crumble - Point-and-Click 2D QEC circuit builder.

Automation tool

• tqec - Design automation tool for tqec.

• LaSsynth - A synthesizer for lattice surgery subroutines.

• Lattice Surgery Compiler - Compile logical quantum circuits to lattice surgery operations on a surface code lattice.

Decoder

• PyMatching - A fast MWPM decoder for quantum error correction code, implemented in C++.

• Fusion Blossom - Another fast MWPM decoder for quantum error correction code, implemented in Rust.

• Belief Matching - An implementation of belief-matching decoder.

• Chromobius - An implementation of a "mobius decoder" for color code.

• ldpc - Belief propagation(BP) implementation, also include implementations for union-find, belief-find and more decoders(in the branch "release-v2").

Tutorials and Talks

• TQEC Group Meetings - Insightful introductory recordings and resources by Austin Fowler and other TQEC group members.
• A Rosetta Stone for the ZX Calculus and the Surface Code - Explain the connection between ZX Calculus and surface code computation by Craig Gidney.
• 3D topological diagram explanation - Unfinished slides of Craig Gidney to explain how to read topological diagram from this post.
• QEC23 - Recording of 6th International Conference on Quantum Error Correction, some talks are about TQEC.

Links

• TQEC Google group - A community for learning about TQEC and building the design automation tools.
• Error Correction Zoo - Collection of classical and quantum error correction codes, including the topological quantum error correction codes.
• Quantum Computing Stack Exchange - Question-and-answer site dedicated to quantum computing, where plenty of TQEC related questions are involved.
• SketchUp - Useful tool to make the space-time diagram for topological logical computation.
• Algorithmic Assertions - Craig Gidney's blogs about computer science and quantum computing, where the topic of TQEC is involved.