DOI: 10.5281/zenodo.18498540
title: Experimental Evidence of Topology-Dependent Error Correlations in Y⊗Z Stabilizer Measurements on IBM's 156-Qubit Heron Processor (4.86σ)

description: Experimental Evidence of Topology-Dependent Error Correlations in Quantum Stabilizer Measurements

This dataset presents experimental measurements of stabilizer consistency across multiple four-qubit modules on a 156-qubit superconducting processor. Using an algebraic parity-triangle test in the Y⊗Z basis, we observe statistically significant, topology-dependent deviations from stabilizer consistency (up to 4.86σ), even when measurement and SPAM effects are controlled. These results provide direct experimental evidence that independent local noise models are insufficient to describe real multi-qubit hardware behavior, motivating hardware-aware approaches to quantum error correction and system design.

Key Discoveries

Module 0 (qubits 0,1,2): 4.86σ deviation (99.9999% confidence)

Discovery-level statistical significance



Measured YZ₀₂: 0.4725 [95% CI: 0.4617-0.4834]

Expected YZ₀₂: 0.4994

Deviation magnitude: 2.68% (0.0268)


Module 2 (qubits 8,9,10): 3.76σ deviation (99.98% confidence)

Independent confirmation



Measured YZ₀₂: 0.5339 [95% CI: 0.5231-0.5447]

Expected YZ₀₂: 0.5132

Deviation magnitude: 2.07% (0.0207)


Overall Results



2 of 6 tested modules (33%) show >3σ deviations from expected consistency

Total measurements: 294,912 quantum circuit executions

QPU time: 77 seconds on state-of-the-art hardware

Job ID: d61v0lao8gvs73f1gutg (publicly verifiable)


Scientific Significance

Connection to 2025 Nobel Prize in Physics

The 2025 Nobel Prize recognized John Martinis, John Clarke, and Michel Devoret for proving that engineered electrical circuits can exhibit quantum behavior—establishing the physical foundation of superconducting quantum computing.

Our work extends this foundation: We demonstrate that when many quantum "artificial atoms" operate together at scale, their error structure exhibits systematic, topology-dependent correlations that challenge simplified noise assumptions commonly used in quantum error correction threshold modeling.

Impact on Quantum Error Correction



Standard QEC threshold calculations typically assume independent local noise models

Our experimental evidence shows topology-dependent deviations from these assumptions

Error correction code design may benefit from incorporating hardware-specific correlation structure

System architects require hardware-aware characterization for optimal performance


Novel Experimental Method

Parity-Triangle Consistency Test

For Y⊗Z stabilizers, the algebraic relation must hold if stabilizer measurements are consistent:









 






YZ₀₁ · YZ₁₂ = YZ₀₂ (mod 2)



We independently measured all three stabilizers:



YZ₀₁: Parity of qubits 0 & 1

YZ₁₂: Parity of qubits 1 & 2

YZ₀₂: Parity of qubits 0 & 2 (triangle completion)


Result: Two modules show statistically significant deviations with confidence levels far beyond random statistical fluctuation.

To our knowledge, this is the first experimental application of a Y⊗Z parity-triangle consistency test on superconducting hardware, enabled by our proprietary π/4 rotation architecture (U.S. Provisional Patent No. 63/952,786).

Experimental Rigor

Platform

IBM Quantum ibm_fez (Heron r2 architecture)



156 qubits total

Heavy-hex topology

Gate error rates on the order of 10⁻³

State-of-the-art superconducting transmon processor


Measurement Protocol



6 four-qubit modules (24 qubits total)

36 circuits (6 per module)

8,192 shots per circuit

Job ID: d61v0lao8gvs73f1gutg (publicly verifiable)


SPAM Controls

State Preparation and Measurement errors were isolated:



Ancilla-only measurements: ~98% fidelity

No-syndrome controls: verified preparation quality

Critical finding: Deviations persist after controlling for static measurement artifacts, indicating dynamic error correlations during circuit execution


Statistical Analysis



Wilson confidence intervals (95%)

Sigma significance testing: σ = (measured - expected) / SE

Publication threshold: >3σ (99.7% confidence)

Our results: 4.86σ and 3.76σ (both well above threshold)


Complete Dataset Contents

Raw Experimental Data



job-d61v0lao8gvs73f1gutg-result.json (98KB) - Complete IBM Quantum circuit results with all measurement outcomes

meta_d61v0lao8gvs73f1gutg.json (5KB) - Circuit metadata including qubit mappings and measurement configurations


Analysis & Results



yz_syndrome_analysis.json - Complete statistical analysis including:



Module-by-module breakdown with confidence intervals

Parity consistency calculations

Sigma significance values

SPAM baseline measurements



module_results_table.csv - Summary table with all 6 modules ranked by performance


Documentation



README.md (11KB) - Comprehensive experimental methodology, results interpretation, theoretical discussion, and reproducibility instructions

YZ-sweep.docx (51KB) - Full experimental report with detailed analysis and publication recommendations

CITATION.cff - Standardized citation metadata

LICENSE - CC BY 4.0 for data, MIT for code


Module Performance Summary






Rank
Module
Qubits
Y⊗Z Fidelity
SPAM
σ
Deviation
Status




1
4
[16,23,22]
61.0%
0.2%
1.89σ
1.05%
✓ Consistent


2
3
[12,13,14]
61.5%
0.8%
1.05σ
0.58%
✓ Consistent


3
1
[4,5,6]
58.7%
1.8%
2.96σ
1.64%
Marginal


4
2
[8,9,10]
61.2%
4.3%
3.76σ
2.07%
⚠️ DEVIATION


5
5
[17,27,26]
57.3%
1.7%
2.35σ
1.30%
Marginal


6
0
[0,1,2]
50.7%
3.8%
4.86σ
2.68%
⚠️ DEVIATION





Overall Statistics



Mean Y⊗Z fidelity: 58.4% ± 4.0%

Mean SPAM penalty: 2.1% ± 1.4%

Mean parity deviation: 1.55%

Maximum significance: 4.86σ

Statistically significant (>3σ): 2/6 modules (33%)


Theoretical Implications

Possible Physical Mechanisms

The observed topology-dependent deviations may arise from several physical mechanisms:



Measurement-induced dephasing: First stabilizer measurement perturbs the system; subsequent measurements see correlated state evolution

Qubit crosstalk: Neighboring qubits interact during readout, creating spatially correlated errors

Leakage to non-computational states: Transmon |2⟩, |3⟩ levels create dynamics beyond standard Pauli noise models

Memory effects in control lines: Microwave pulse reflections, cavity photon lifetimes, residual couplings


These mechanisms can produce non-Markovian error correlations—errors with memory of previous operations that propagate through multi-qubit circuits in systematic, hardware-dependent ways.

Supporting Evidence for Correlation Structure



Module 0 (highest σ) has lowest overall fidelity → hardware quality correlation

Module 2 (second highest σ) has high fidelity elsewhere → not simply systematic gate errors

Deviations ~2-3% relative → consistent with known crosstalk magnitudes

Topology-dependent: different physical regions show different correlation behavior


Why This Matters for Industry

Significance for Advanced Quantum Hardware

Our observations on IBM's Heron r2 architecture (heavy-hex topology, gate errors ~10⁻³) demonstrate that correlation effects persist even in state-of-the-art hardware. This is not a limitation of early quantum computers—these are fundamental features of multi-qubit system dynamics that require hardware-aware approaches.

Impact on Stakeholders



Hardware vendors: Topology-aware qubit selection and calibration protocols can identify and mitigate correlation-prone regions

QEC researchers: Incorporating hardware-specific correlation structure may improve threshold estimates and code performance

Algorithm designers: Runtime characterization enables intelligent qubit allocation and error-aware compilation

System architects: Hardware abstraction layers (e.g., Q-HAL) that account for topology-dependent behavior become essential for scaling


Reproducibility & Verification

Independent Verification

All results can be verified using IBM Quantum job ID: d61v0lao8gvs73f1gutg

Complete Reproducibility



Raw data provided: All 294,912 measurement outcomes

Analysis scripts included: Rerun statistical analysis

Circuit generation code: Reproduce experiment on any IBM backend

Metadata preserved: Complete qubit mappings and configurations


Requirements









 






pip install qiskit qiskit-ibm-runtime numpy scipy



Data Availability & Licensing

Open Access

All data is freely available under Creative Commons Attribution 4.0 International (CC BY 4.0)

Code License

Analysis scripts under MIT License

Patent Protection

The Y⊗Z stabilizer preparation method using π/4 rotations is protected under U.S. Provisional Patent Application No. 63/952,786. This dataset demonstrates experimental validation but does not disclose enabling technical details.

Usage

You are free to use, modify, and build upon this dataset for any purpose, including commercial, as long as you provide attribution.

Research Context



Organization: Quantum-Clarity LLC

Platform: QuantaCore™ quantum control system

Technology: Q-HAL (Quantum Hardware Abstraction Layer) for topology-aware optimization

Website: https://www.quantum-clarity.com/quantum-reliability


Contact & Collaboration

Principal Investigator: Quantum-Clarity LLCEmail: info@quantum-clarity.com

Collaboration Opportunities



Theoretical modeling of correlation mechanisms

Cross-platform validation (IonQ, Rigetti, trapped ions)

Extended studies on larger systems

QEC code development incorporating correlation structure

Hardware-aware compilation strategies


Acknowledgments



IBM Quantum for hardware access and QPU credits

IBM Quantum team for technical support

The quantum computing research community


Related Publications



Martinis, J., Clarke, J., & Devoret, M. (2025). Quantum behavior in macroscopic superconducting circuits. Nobel Prize in Physics 2025.

Quantum-Clarity 116-qubit Y⊗Z demonstration (previous work establishing the measurement architecture)


Version History

v1.0 (February 5, 2026) - Initial public release



Complete experimental dataset from February 4, 2026

6 modules, 294,912 measurements

Statistical analysis with 4.86σ discovery

Full documentation and reproducibility scripts