Physics-Informed Neural Networks with Adaptive Constraints for Multi-Qubit Quantum Tomography
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| Format: | Preprint |
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2025
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| _version_ | 1866917148638576640 |
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| author | Feng, Changchun Tao, Laifa Chen, Lin |
| author_facet | Feng, Changchun Tao, Laifa Chen, Lin |
| contents | Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating quantum mechanical constraints via adaptive weighting, a residual-and-attention-enhanced architecture, and differentiable Cholesky parameterization for physical validity. Evaluations on 2--5 qubit systems and arbitrary-dimensional states show PINN consistently outperforms traditional neural networks (TNNs), achieving highest fidelity across all dimensions. PINN outperforms baselines, with marked improvements in moderately high-dimensional systems, superior noise robustness (slower performance degradation), and consistent dimensional robustness. Theoretical analysis shows physical constraints reduce Rademacher complexity and mitigate the curse of dimensionality via constraint-induced dimension and sample complexity reduction, effective regardless of qubit number. While experiments are limited to 5-qubit systems due to computational constraints, our theoretical framework (convergence guarantees, generalization bounds, scalability theorems) justifies PINN's advantages will persist and strengthen in larger systems (6+ qubits), where constraint-induced dimension reduction benefits grow with system size. Practically, this advances quantum error correction and gate calibration by reducing measurement requirements from O(4^n) to O(2^n) while maintaining high fidelity, enabling faster error correction cycles and accelerated calibration critical for scalable quantum computing. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Neural Networks with Adaptive Constraints for Multi-Qubit Quantum Tomography Feng, Changchun Tao, Laifa Chen, Lin Quantum Physics Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating quantum mechanical constraints via adaptive weighting, a residual-and-attention-enhanced architecture, and differentiable Cholesky parameterization for physical validity. Evaluations on 2--5 qubit systems and arbitrary-dimensional states show PINN consistently outperforms traditional neural networks (TNNs), achieving highest fidelity across all dimensions. PINN outperforms baselines, with marked improvements in moderately high-dimensional systems, superior noise robustness (slower performance degradation), and consistent dimensional robustness. Theoretical analysis shows physical constraints reduce Rademacher complexity and mitigate the curse of dimensionality via constraint-induced dimension and sample complexity reduction, effective regardless of qubit number. While experiments are limited to 5-qubit systems due to computational constraints, our theoretical framework (convergence guarantees, generalization bounds, scalability theorems) justifies PINN's advantages will persist and strengthen in larger systems (6+ qubits), where constraint-induced dimension reduction benefits grow with system size. Practically, this advances quantum error correction and gate calibration by reducing measurement requirements from O(4^n) to O(2^n) while maintaining high fidelity, enabling faster error correction cycles and accelerated calibration critical for scalable quantum computing. |
| title | Physics-Informed Neural Networks with Adaptive Constraints for Multi-Qubit Quantum Tomography |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.14543 |