A Physics-Informed Neuro-Fuzzy Framework for Quantum Error Attribution

TL;DR

This work establishes a robust, interpretable diagnostic layer that prevents error mitigation techniques from being applied to logically flawed circuits and introduces the Bhattacharyya Veto, a hard physical constraint grounded in the Data Processing Inequality that prevents the classifier from attributing topologically impossible output distributions to noise.

Abstract

As quantum processors scale beyond 100 qubits, distinguishing software bugs from stochastic hardware noise becomes a critical diagnostic challenge. We present a neuro-fuzzy framework that addresses this attribution problem by combining Adaptive Neuro-Fuzzy Inference Systems (ANFIS) with physics-grounded feature engineering. We introduce the Bhattacharyya Veto, a hard physical constraint grounded in the Data Processing Inequality that prevents the classifier from attributing topologically impossible output distributions to noise. Validated on IBM's 156-qubit Heron r2 processor (ibm_fez) across 105 circuits spanning 17 algorithm families, the framework achieves 89.5% effective accuracy (+/- 5.9% CI). The system implements a safe failure mode, flagging 14.3% of ambiguous cases for manual review rather than forcing low-confidence predictions. We resolve key ambiguities -- such as distinguishing correct Grover amplification from bug-induced collapse -- and identify fundamental limits of single-basis diagnostics, including a Z-basis blind spot where phase-flip errors remain statistically invisible. This work establishes a robust, interpretable diagnostic layer that prevents error mitigation techniques from being applied to logically flawed circuits.

Figures (11)

• Figure 1: ANFIS Architecture: The 5-Layer Neuro-Fuzzy Stack
• Figure 2: Classification Decision Logic: Veto check followed by ANFIS thresholds
• Figure 3: Classification outcomes for the 105-circuit validation suite on IBM Heron. The framework achieved 89.5% effective accuracy.
• Figure 4: Decision logic mapped onto the feature space. The horizontal band above $D_B^{\mathrm{log}} = 0.20$ represents the veto region where circuits are classified as SOFTWARE_BUG before ANFIS evaluation. Below the veto threshold, probability boundaries at $P(\text{noise}) = 0.35$ and $0.70$ partition the space into bug, uncertain, and noise regions.
• Figure 5: Resolution of the Grover boundary problem. (a) Actual Grover circuits from the validation set, with correctly classified circuits in green and errors in red. (b) Conceptual illustration: both a correct Grover search and a buggy "collapse" circuit produce low measured entropy, but only the buggy circuit shows high entropy deviation because its expected output should have been a superposition.