Distributional Robustness of Parameterized Quantum Circuits: A Wasserstein-2 Study on NISQ Hardware
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901274261192704 |
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| author | Davis, Devin Phillip |
| author_facet | Davis, Devin Phillip |
| contents | <p>We introduce a hardware-native robustness metric for parameterized quantum circuits (PQCs) based on the Wasserstein-2 (<span class="math-inline">$W_2$</span>) distance between output probability distributions across replicates, requiring no classical simulation or ideal-state reference. We apply this framework to a golden-spiral entanglement circuit on a 27-qubit subset of <code>ibm_fez</code> (156-qubit IBM Heron r2 processor), sweeping the initial rotation angle. The central hypothesis — that the square of the golden ratio provides superior distributional robustness — is falsified: the lower-angle configuration achieves 28% higher robustness. A strong inverse correlation between output entropy and distributional robustness is observed, suggesting that conservative parameterization — which preserves low-entropy structured attractors — provides greater shot-to-shot reproducibility on NISQ hardware than maximally expressive parameterizations. We characterize the mechanism: the low-angle circuit preserves a 112×-enhanced probability mode at the all-ones computational basis state, while the high-entropy circuits produce near-uniform distributions with large inter-replicate variation. These results have implications for noise-aware circuit design, VQE/QAOA initialization, and NISQ benchmarking methodology.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19864030 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Distributional Robustness of Parameterized Quantum Circuits: A Wasserstein-2 Study on NISQ Hardware Davis, Devin Phillip <p>We introduce a hardware-native robustness metric for parameterized quantum circuits (PQCs) based on the Wasserstein-2 (<span class="math-inline">$W_2$</span>) distance between output probability distributions across replicates, requiring no classical simulation or ideal-state reference. We apply this framework to a golden-spiral entanglement circuit on a 27-qubit subset of <code>ibm_fez</code> (156-qubit IBM Heron r2 processor), sweeping the initial rotation angle. The central hypothesis — that the square of the golden ratio provides superior distributional robustness — is falsified: the lower-angle configuration achieves 28% higher robustness. A strong inverse correlation between output entropy and distributional robustness is observed, suggesting that conservative parameterization — which preserves low-entropy structured attractors — provides greater shot-to-shot reproducibility on NISQ hardware than maximally expressive parameterizations. We characterize the mechanism: the low-angle circuit preserves a 112×-enhanced probability mode at the all-ones computational basis state, while the high-entropy circuits produce near-uniform distributions with large inter-replicate variation. These results have implications for noise-aware circuit design, VQE/QAOA initialization, and NISQ benchmarking methodology.</p> |
| title | Distributional Robustness of Parameterized Quantum Circuits: A Wasserstein-2 Study on NISQ Hardware |
| url | https://doi.org/10.5281/zenodo.19864030 |