Transition from Statistical to Hardware-Limited Scaling in Photonic Quantum State Reconstruction
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908882164514816 |
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| author | Baumann, Attila Kis, Zsolt Koltai, János Vattay, Gábor |
| author_facet | Baumann, Attila Kis, Zsolt Koltai, János Vattay, Gábor |
| contents | The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental discovery of a fundamental accuracy bound on integrated photonic processors: a ``Hardware Horizon'' where the reconstruction error undergoes a sharp phase transition. While the error initially obeys the predicted statistical scaling $\mathcal{O}(M^{-1/2})$, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this intrinsic noise floor imposes a hard bound that statistical accumulation cannot overcome. These findings establish that the utility of shadow tomography on NISQ (noisy intermediate-scale quantum) hardware is defined by a specific scaling law involving hardware parameters, necessitating active compensation strategies to bridge the gap between theoretical purity and the noisy reality of integrated photonics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12235 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transition from Statistical to Hardware-Limited Scaling in Photonic Quantum State Reconstruction Baumann, Attila Kis, Zsolt Koltai, János Vattay, Gábor Quantum Physics Disordered Systems and Neural Networks Emerging Technologies Optics The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental discovery of a fundamental accuracy bound on integrated photonic processors: a ``Hardware Horizon'' where the reconstruction error undergoes a sharp phase transition. While the error initially obeys the predicted statistical scaling $\mathcal{O}(M^{-1/2})$, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this intrinsic noise floor imposes a hard bound that statistical accumulation cannot overcome. These findings establish that the utility of shadow tomography on NISQ (noisy intermediate-scale quantum) hardware is defined by a specific scaling law involving hardware parameters, necessitating active compensation strategies to bridge the gap between theoretical purity and the noisy reality of integrated photonics. |
| title | Transition from Statistical to Hardware-Limited Scaling in Photonic Quantum State Reconstruction |
| topic | Quantum Physics Disordered Systems and Neural Networks Emerging Technologies Optics |
| url | https://arxiv.org/abs/2603.12235 |