NISQ processors operate as noisy open systems where the Born rule silently fails. modularq detects, quantifies, and corrects nonequilibrium measurement bias — without touching your circuits or hardware.
modularq sits between your measurement output and your analysis pipeline. It requires only the reconstructed reduced state — no hardware access, no circuit modifications.
Compute the modular generator K = −log(ρ) from the reconstructed reduced state. Extract outcome-resolved modular imbalances δK_i that reveal nonequilibrium structure invisible to standard Born pipelines.
Compute the Modular Imbalance Score (MIS) — a single, dimensionless number that classifies your measurement regime: Born-valid, perturbative nonequilibrium, or non-KMS. Comparable across devices and backends.
Apply a universal, normalization-preserving exponential reweighting of Born probabilities. Selected automatically via AIC model comparison — only applied when the data supports it. Fully falsifiable.
The MIS is modularq's core diagnostic — a scalar, dimensionless benchmark that tells you exactly how far your measurement process is from KMS equilibrium. Low MIS means Born is valid. High MIS means you need correction.
Validated on real IBM Quantum hardware across ibm_fez, ibm_marrakesh, and ibm_torino. Published data available at Zenodo DOI: 10.5281/zenodo.18066279.
Drop-in augmentation for Qiskit, Cirq, and Braket-compatible workflows. No changes to circuit semantics or hardware control.
Analysis of 128 measurements from IBM Quantum processors. modularq correctly identifies nonequilibrium regimes and applies corrections only when statistically warranted.
| Backend | Shots (N) | MIS | Regime | Model | ΔAIC | p(0) Born → Modular |
|---|---|---|---|---|---|---|
| ibm_fez | 100,000 | 0.0079 | KMS BALANCED | MODULAR | +4.24 | 0.5000 → 0.5039 |
| ibm_fez | 100,000 | 0.0040 | KMS BALANCED | EMPATE | −0.43 | 0.5000 → 0.5020 |
| ibm_fez | 2,000 | 0.0611 | PERTURBATIVE | MODULAR | +5.45 | 0.5000 → 0.5305 |
| ibm_fez | 2,000 | 0.0350 | PERTURBATIVE | EMPATE | +0.45 | 0.5000 → 0.5175 |
| ibm_marrakesh | 2,000 | 0.0280 | PERTURBATIVE | EMPATE | −0.43 | 0.5000 → 0.4860 |
modularq is open source and free for academic and non-commercial use. Commercial deployments require a license agreement.
Whether you're running VQE, benchmarking backends, or building quantum software — modularq adds a physically grounded diagnostics layer to your existing workflow.
cb@balfagonresearch.org