Physics-Informed Neural Networks with Adaptive Constraints for Multi-Qubit Quantum Tomography

TL;DR

This paper introduces a physics-informed neural network framework with adaptive constraints for quantum state tomography, significantly improving accuracy, noise robustness, and scalability in multi-qubit systems, thus advancing practical quantum computing.

Contribution

The paper develops a novel PINN architecture with adaptive quantum constraints, residual attention, and differentiable parameterization, providing theoretical guarantees and superior empirical performance for multi-qubit quantum tomography.

Findings

PINN achieves higher fidelity than traditional neural networks across 2-5 qubits.

PINN demonstrates enhanced noise robustness and dimensional scalability.

Theoretical analysis confirms reduced sample complexity and improved generalization in larger systems.

Abstract

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.