Algorithm Index
This index maps each implemented QEC scheme or decoder to its documentation, source files, examples, tests, and current modeling limits.
| Scheme | Protects against / purpose | Main files | Examples | Tests | Limits |
|---|---|---|---|---|---|
| 3-qubit bit-flip repetition | One Pauli-X error on three physical qubits | encode_bitflip.m, syndrome_bitflip.m, correct_bitflip.m, recover_bitflip.m |
minimal_bitflip_recovery.m, plot_logical_vs_p.m, plot_noisy_syndrome_rounds.m |
test_bitflip.m, test_decoders_and_simulations.m |
Bit-flip protection only; noisy syndrome mode models classical readout flips |
| 3-qubit phase-flip repetition | One Pauli-Z error using X-basis repetition | encode_phaseflip.m, syndrome_phaseflip.m, correct_phaseflip.m, recover_phaseflip.m |
minimal_phaseflip_recovery.m |
test_phaseflip.m |
Phase-flip protection only; no dedicated plot script |
[[[4,2,2]] error-detecting code](algorithms/FOUR_TWO_TWO.md) |
Detects any single-qubit Pauli X/Y/Z error; encodes two logical qubits | four_two_two_stabilizers.m, encode_four_two_two.m, syndrome_four_two_two.m, detect_four_two_two.m |
minimal_four_two_two_detection.m |
test_stabilizer_codes.m |
Detection only; zero-syndrome logical operators are not corrected |
| 5-qubit perfect code | Any single-qubit Pauli X/Y/Z error | fivequbit_stabilizers.m, encode_fivequbit.m, syndrome_fivequbit.m, correct_fivequbit.m, recover_fivequbit.m |
minimal_fivequbit_recovery.m |
test_stabilizer_codes.m |
State-vector stabilizer projection, not an encoding circuit |
| 7-qubit Steane code | Any single-qubit Pauli X/Y/Z error with CSS checks | steane_parity_check.m, encode_steane.m, syndrome_steane.m, correct_steane.m, recover_steane.m |
minimal_steane_recovery.m |
test_stabilizer_codes.m |
Direct projective checks; transversal gates are not implemented |
| 7-qubit triangular color code | Smallest triangular color code; any single-qubit Pauli X/Y/Z error | color7_layout.m, color7_stabilizers.m, encode_color7.m, recover_color7.m, recover_color7_pauli.m |
minimal_color7_recovery.m |
test_color7.m |
Uses the standard Steane-equivalent [7,1,3] color-code representation |
| 9-qubit Shor code | Any single-qubit Pauli X/Y/Z error using bit/phase repetition structure | encode_shor.m, syndrome_shor.m, correct_shor.m, recover_shor.m |
minimal_shor_recovery.m |
test_stabilizer_codes.m |
No fault-tolerant syndrome-extraction circuit |
| 3x3 Bacon-Shor subsystem code | Single-qubit Pauli errors in a compact subsystem-code Pauli-frame model | bacon_shor_x_syndrome.m, bacon_shor_z_syndrome.m, decode_bacon_shor_x.m, decode_bacon_shor_z.m, recover_bacon_shor_pauli.m |
minimal_bacon_shor_recovery.m |
test_bacon_shor.m |
Tracks Pauli-frame logical success rather than full gauge-state fidelity |
| 1D repetition decoder | Minimum-weight binary chain compatible with a parity syndrome | decode_repetition_min_weight.m, decode_majority.m |
minimal_repetition_decoder.m |
test_decoders_and_simulations.m |
Binary nearest-neighbor parity decoder only; no soft information |
| Surface-3 prototype | Compact surface-code-style X/Z/Pauli code-capacity and noisy-syndrome studies | surface3_*, decode_surface3_*, simulate_surface3_*, sweep_surface3_* |
minimal_surface3_syndrome.m, minimal_surface3_circuit_level.m, surface3_walkthrough.m |
test_surface3.m |
Educational prototype, not a calibrated threshold simulator |
| Generic surface-layout decoder | Odd-distance square layout and lightweight decoder comparisons | surface_layout.m, surface_syndrome.m, decode_surface_min_weight.m, decode_surface_mwpm.m, decode_surface_graph_matching.m, decode_surface_union_find.m, sweep_surface_distance_logical_error.m |
minimal_surface_distance_decoder.m, benchmark_surface_distance_decoder.m, plot_surface_distance_scaling.m |
test_surface_distance.m |
Cached exact/bounded lookup, MWPM-style small-defect matching, bounded syndrome-graph baseline, and larger-distance peeling heuristic |
Validation Commands
Run all unit tests:
octave --no-gui tests/run_all_tests.mRun all text examples:
octave --no-gui examples/run_text_examples.mRegenerate the compact simulation report:
octave --no-gui examples/generate_simulation_report.m