QGDecoder is a graph-aware bounded distance quantum decoder supporting arbitrary stabilizer codes under depolarization channel.

• An $[[N,k,d]]$ quantum code corrects upto weight $t=(d-1)/2$ errors with certainty.
• QGDecoder takes in a tunable target weight $T$. If $T\leq t$ it ensures all errors with weight $w\leq T$ are corrected.
• Graph state based bounded distance decoding.
• Additive.h supports both CSS and non-CSS codes.
• Use CSS.h for improved efficiency with CSS codes.

Package features and requirements

• Header only package. Make sure the parent folder QGDecoder is accessible in you project file. Enjoy decoding!
• Written in C++ (use C++17 preferably).
• Linear algebra powered by Armadillo. Install from here to use QGDecoder.

Usage

• Provide set of $N-k$ stabilizers (stabs) and $k$ logical operators (Lz and Lx) as C++ vector of strings of length $N$.
• Use only "X", "Y", "Z" or "I" to give the Pauli component e.g. "XZZXI" for five qubits.
• The struct stab_to_graph object S(stabs,Lz,Lx,d) returns the equivalent graph of the code
• By default Lz logicals are appended with stabs. Pass a boolean false as fifth argument to use Lx.
• get_pauli_error_vector(N,w,p,error_type,seed_random) returns a random Pauli error string on $N$ qubits having atmost weight $w$ with single qubit error channel probability $p$. error_type='D'/'X'/'Y'/'Z' enables depolarisation/bit-flip/bit-phase flip/phase flip errors. Set random seeding with seed_random if not given system generated seed is used.

Additive

• get_stabilizer_syndrome(E,S,stab_syn) returns the stabilizer syndrome stab_syn corresponding to Pauli error E.
• get_graph_syndrome(stab_syn,S,graph_syn) maps to the graph syndrome graph_syn.
• decode(graph_syn,T,S) decodes the graph syndrome with BDD target weight T and returns the correction C.

CSS

• Use functions from CSS.h for CSS codes to get better efficiency by utilizing bipartite graph structure.

• get_stabilizer_syndrome_CSS(E,S,stab_syn) returns the stabilizer syndrome stab_syn corresponding to Pauli error E.

• get_graph_syndrome_CSS(stab_syn,S,graph_syn_Z,graph_syn_X) maps to the Z and X graph syndromes graph_syn_Z,graph_syn_X.

• decode_CSS(graph_syn_Z,graph_syn_X,T,S) decodes the graph syndromes with BDD target weight T and returns the correction C.

• logical_error(E,C,Lz,Lx) returns true if there is an occurrence of logical error after the correction C.

• Just run the script files non-CSS.sh and CSS.sh to a simple demo.

Standard quantum codes available with QGDecoder

• non-CSS optimal codes of distance $d=3,5,7,9,11$.
• non-CSS XZZX code on $d\times d$ square lattice.
• CSS triangular color code on triangular lattice of length $d$.
• CSS rotated surface codes on $d\times d$ square lattice.

Attribution

When using QGDecoder, please cite our paper:

@misc{QGDecoder,
title={A graph-aware bounded distance decoder for all stabilizer codes}, 
author={Harikrishnan K J and Amit Kumar Pal},
year={2026},
eprint={2604.25424},
archivePrefix={arXiv},
primaryClass={quant-ph},
url={https://arxiv.org/abs/2604.25424}, 
}