Holographic Bio-Adaptive Quantum Error Correction
A research project connecting three ideas:
- Ryu-Takayanagi geometry — using holographic entropy gaps from AdS/CFT as decoder priors
- Bio-adaptive weight modulation — immune-system-inspired CDR3-length priors for MWPM
- Real IBM Quantum hardware validation — two runs on Heron r2 processors, 60,000 total shots
| Date | Machine | Processor | Shots | Physical Error Rate | Logical Errors |
|---|---|---|---|---|---|
| Nov 21, 2025 | ibm_torino | 133q Heron r1 | 30,000 | 8.05% | 0.04% |
| Mar 17, 2026 | ibm_marrakesh | 156q Heron r2 | 30,000 | 0.11% | 0.00% |
The March 2026 run produced zero logical errors across 30,000 shots. Majority-vote QEC corrected every single-qubit flip. The 73× improvement in physical error rate over four months tracks IBM's Heron r2 hardware progress in real time.
Per-qubit noise asymmetry observed on ibm_marrakesh: q[14] had 3× higher error rate than q[7] and q[8] — a direct motivation for noise-matched adaptive decoders.
| Decoder | Threshold p_th | Noise Models |
|---|---|---|
| Standard MWPM | 0.00617 ± 0.00009 | depolarizing, correlated, leakage |
| Bio-Adaptive (CDR3 prior) | 0.00617 ± 0.00009 | — |
| HoloBA (RT prior) | 0.00617 ± 0.00009 | Δp_th = 0.000 ± 0.00013 |
Primary finding: The RT Boltzmann prior is structurally well-defined — the bound p_L ≤ exp(−ΔS_RT) holds under two postulates — but produces no threshold improvement at d=3, d=5. Only 3 of 116 DEM fault edges carry ΔS_RT > 0 at d=3 (near-uniform prior). The null result predicts a detectable signal at d≥7, where more DEM edges cross the logical min-cut surface.
holoba-qec/
│
├── hardware/ ← Real IBM Quantum experiment
│ ├── ibm_hardware_test_v2.py ← Submit & retrieve jobs (updated for 2026 API)
│ ├── data/
│ │ ├── ibm_marrakesh_mar17_2026_30k.pkl ← Mar 2026 run (99.89% fidelity)
│ │ └── ibm_torino_nov21_2025_30k.pkl ← Nov 2025 baseline
│ └── results/
│ └── ibm_torino_fidelity_map.png
│
├── src/ ← Python decoder implementations
│ ├── holoba_decoder.py ← HoloBA: MWPM + RT prior weight modulation
│ ├── rt_prior.py ← Ryu-Takayanagi entropy gap computation
│ └── bio_adaptive_decoder.py ← CDR3 immune-inspired decoder prototype
│
├── decoders/ ← Rust decoder implementations
│ ├── adaptive-mwpm-core/ ← Verified production decoder (Phase 1 baseline)
│ │ ├── src/
│ │ ├── Cargo.toml
│ │ └── surface_code_d3.json
│ └── bio-adaptive-explorer/ ← Early research prototype (Tests A–H)
│ └── src/
│
├── benchmarks/
│ ├── baseline_benchmark.py ← Standard MWPM threshold (p_th = 0.00617)
│ ├── holoba_phase4_benchmark.py ← HoloBA alpha sweep + threshold curves
│ ├── surface_code_d3.json
│ └── surface_code_d5.json
│
├── tests/
│ ├── test_holoba_decoder.py ← 3/3 pass
│ └── test_rt_prior.py ← 4/4 pass
│
├── results/
│ ├── figures/
│ │ ├── holoba_threshold_d3_d5.pdf ← Main threshold figure
│ │ └── holoba_threshold_d3_d5.png
│ ├── holoba_phase4_depolarizing.csv
│ ├── holoba_phase4_correlated.csv
│ ├── holoba_phase4_leakage.csv
│ └── holoba_phase4_alpha_sweep.csv
│
├── paper/ ← LaTeX manuscript (target: PRX Quantum)
│ ├── main.tex
│ ├── abstract.tex
│ ├── introduction.tex
│ ├── methods.tex
│ ├── results.tex
│ ├── discussion.tex
│ ├── conclusions.tex
│ ├── holographic.tex
│ ├── appendix_a/b/c.tex
│ └── figures/
│
├── notes/
│ ├── bhi_connection.md ← 3 structural correspondences to BHI paradox
│ └── rt_bound_derivation.md ← Proof of p_L ≤ exp(−ΔS_RT)
│
├── references/
│ └── references.bib
│
└── requirements.txt
git clone https://github.com/ChuckGPTX/holoba-qec.git
cd holoba-qec
pip install -r requirements.txt
# Run the baseline benchmark
python benchmarks/baseline_benchmark.py
# Run HoloBA vs MWPM threshold sweep
python benchmarks/holoba_phase4_benchmark.py
# Run all tests
python -m pytest tests/# Authenticate once (token from https://quantum.cloud.ibm.com/account)
python3 -c "
from qiskit_ibm_runtime import QiskitRuntimeService
QiskitRuntimeService.save_account(
token='YOUR_TOKEN',
instance='crn:v1:bluemix:public:quantum-computing:...',
channel='ibm_quantum_platform',
overwrite=True
)
"
# Submit (Step A), retrieve (Step B), and decode (Step C) — see script for details
python hardware/ibm_hardware_test_v2.pyThe hardware script is designed for the current IBM Quantum Platform (quantum.cloud.ibm.com) and uses generate_preset_pass_manager per the 2026 API. See hardware/ibm_hardware_test_v2.py for full documentation.
The verified production decoder used as the benchmark baseline. Accepts syndromes in Stim format, loads chip topology from JSON, outputs FLIP_Q{n} / NO_CORRECTION. Phase 1 verified 2026-03-15. ~3.2M shots/sec.
The early research prototype. Built after the first IBM Torino run, it contains Tests A–H that discovered the key ideas (per-qubit noise weighting, syndrome caching, online learning). Performance claims in its README are exploratory, not independently benchmarked. Kept as a record of the research process.
src/holoba_decoder.py implements:
w_holoBA(e) = log((1-p_e)/p_e) + α · ΔS_RT(e)
where ΔS_RT(e) is the Ryu-Takayanagi entropy gap for fault edge e. At α=0, reduces to standard MWPM.
The bound p_L ≤ exp(−ΔS_RT) is derived in notes/rt_bound_derivation.md under two postulates:
- Assumption 1: The DEM fault graph is identified as an effective holographic bulk
- Assumption 2: The surface code satisfies complementary recovery (BKK condition)
Three structural correspondences to the black-hole information paradox are documented in notes/bhi_connection.md.
- Does ΔS_RT provide detectable threshold improvement at d=7+?
- Can a noise-matched decoder (real per-qubit calibration data as priors) outperform MWPM on ibm_marrakesh's asymmetric noise profile?
- What is the IBM hardware improvement trajectory — when does the physical error rate reach the regime where adaptive decoders are distinguishable from MWPM?
@software{holoba_qec,
author = {Crawley, Chuck},
title = {HoloBA-QEC: Holographic Bio-Adaptive Quantum Error Correction},
year = {2026},
url = {https://github.com/ChuckGPTX/holoba-qec},
note = {IBM Marrakesh hardware run: March 17, 2026. 30,000 shots, 0 logical errors.}
}- Ryu, Takayanagi (2006) — Holographic derivation of entanglement entropy, PRL 96, 181602
- Almheiri, Dong, Harlow (2015) — Bulk locality and QEC in AdS/CFT, JHEP
- Harlow (2017) — The RT formula from quantum error correction
- Gidney (2021) — Stim: A fast stabilizer circuit simulator, Quantum 5, 497
- Higgott (2022) — PyMatching: MWPM decoder, ACM TQC
Built by @ChuckGPTX First hardware run: Nov 21, 2025 — ibm_torino Second hardware run: Mar 17, 2026 — ibm_marrakesh (99.89% fidelity, 0 logical errors)