operator_loschmidt_echo_70x1872, H²Q thermodynamic error mitigationBy: Independent Research #90
Description
Name
Kenneth A Mendoza
Circuit
operator_loschmidt_echo_70x1872
Observable value
0.0004
Error bound (low)
-0.016
Error bound (high)
+0.016
Method
H²Q thermodynamic error mitigation
Method proof
Patent Reference: US Provisional Application 63/927,371 (Nov 29, 2025)
Patent details: https://kenmendoza.com/patents
Implementation Repository: https://github.com/bengoechea/H2Q-Thermodynamic-Error-Mitigation
Method Explanation
H²Q thermodynamic error mitigation treating syndromes as thermal fluctuations with hysteresis-based filtering (φ = 2.67). H²Q applies dual-threshold hysteresis gates with dwell-time enforcement to achieve 79.7% false positive reduction in quantum error correction.
Key Features:
- Domain-specific threshold ratio: φ = 2.67 (derived from measurement disturbance)
- Dwell-time enforcement: τ = 60-300 seconds
- Asymmetric thresholds: θ_up = θ_base × 2.67, θ_down = θ_base / 2.67
Validation Results:
- False Positive Reduction: 79.7% (validated on ibm_fez, ibm_torino)
- Statistical Significance: Cohen's d = 10.59, p < 0.0001
- Hardware Validated: IBM ibm_fez (156-qubit), ibm_torino (133-qubit Heron r2)
Observable
Z_52 Z_59 Z_72
Results
For operator_loschmidt_echo_70x1872, H²Q thermodynamic error mitigation on IBM Quantum reports ⟨O⟩ = 0.0004 ± 0.016 based on 10 hardware runs (6 runs at 1024 shots, 3 runs at 4096 shots, 1 run at 8192 shots) on backend ibm_fez. Total compute time: < 10 minutes (within IBM Quantum free access window). Job IDs: d4ps8frher1c73bakq70, d4ps8hnt3pms7396j020, d4ps8j7t3pms7396j040, d4ps8kk5fjns73cvoomg, d4ps8m3her1c73bakqdg, d4pthtsfitbs739gdd00, d4puf9ft3pms7396l61g, d4puo87t3pms7396lef0, d4puo9nt3pms7396leh0, d4puobkfitbs739geheg. The full pipeline, raw data, and aggregation code are in https://github.com/bengoechea/H2Q-Thermodynamic-Error-Mitigation (see HARDWARE_VALIDATION.md and results/).
Interpretation and Caveats: The reported observable value ⟨O⟩ = 0.0004 ± 0.016 is consistent with zero within uncertainty. Analysis of all 10 runs reveals uniform (maximally mixed) bitstring distributions across all shot counts (1024-8192), which may indicate: (1) the circuit operates in a high-noise regime where noise dominates signal, (2) insufficient shot counts to resolve structure above noise, or (3) the Loschmidt echo circuit naturally measures quantum coherence rather than state populations. This submission demonstrates H²Q thermodynamic error mitigation methodology on real hardware with rigorous statistical validation (10 independent runs, shot-weighted aggregation, 95% confidence intervals). However, the uniform distribution suggests this validates H²Q's conservative filtering approach (preserving all states when signal structure is unclear) more than it demonstrates quantum advantage over classical methods for this specific circuit instance. Future work with higher shot counts, different circuit types producing structured outputs (e.g., VQE), or baseline comparisons (ZNE, CDR) would strengthen quantum advantage claims.
Authors
Kenneth A Mendoza
Institutions
Independent Research
Quantum runtime (seconds)
600
Classical runtime (seconds)
No response
Compute resources (quantum)
IBM ibm_fez (156-qubit), ibm_torino (133-qubit Heron r2)
Compute resources (classical)
No response
Notes
10 runs on IBM ibm_fez, full details in Method proof