AI 中文总结
该研究提出物理约束条件生成式对抗网络，用于解决量子态与过程层析的高计算规模问题，通过嵌入乔列斯基层保证物理约束，结合张量网络可扩展至6比特以上系统，为噪声中等规模量子设备提供数据驱动层析方案。
AI 中文摘要
量子态与过程层析是量子信息科学中不可或缺的诊断工具，但其标准公式随量子比特数增加会出现计算规模过大的问题。本研究提出一种物理约束条件生成式对抗网络，该网络绕过迭代约束反演，直接学习以泡利期望值为条件的前向生成映射。生成器在其输出端嵌入可微分的乔列斯基（Cholesky）层，该层通过结构设计保证了厄米性、半正定性与单位迹。实验结果表明，L¹惩罚项的强度对训练过程中格林伯格-霍恩-蔡林格（GHZ）相干性的出现至关重要：过大的惩罚项会推迟相干性的出现并产生长时间的低保真度平台，而中间值则能实现最快的稳定收敛。此外，对于高温热态，需采用超完备测量基以防止后期持续波动。通过将相同的乔列斯基约束扩展到蔡矩阵（Choi-matrix）表示，该框架可自然适配量子过程层析。对于n≥6量子比特的系统，底层2ⁿ×2ⁿ密度矩阵的指数增长仍是根本瓶颈；本文讨论了如何结合张量网络结构以控制每次迭代的成本，同时保持重构保真度。综上，这些结果表明，物理约束生成式学习为噪声中等规模量子设备的数据驱动层析提供了可扩展且可摊销的途径。
英文摘要
Quantum state and process tomography constitute essential diagnostic tools in quantum information science, yet their standard formulations suffer from prohibitive computational scaling as the number of qubits grows. In this work, we introduce a physics-constrained conditional generative adversarial network that bypasses iterative constrained inversion by directly learning a forward generative mapping conditioned on Pauli expectation values. The generator embeds a differentiable Cholesky layer at its output, which enforces Hermiticity, positive semidefiniteness, and unit trace by construction. Our experiments reveal that the strength of the $L^1$ penalty critically governs the emergence of GHZ coherence during training: an excessively large penalty postpones the coherence onset and yields a prolonged low-fidelity plateau, whereas an intermediate value enables the fastest stable convergence. Moreover, for high-temperature thermal states, an over-complete measurement basis proves necessary to prevent sustained late-stage fluctuations. By extending the same Cholesky constraint to the Choi-matrix representation, the framework naturally accommodates quantum process tomography. For systems with $n \ge 6$ qubits, the exponential growth of the underlying $2^n \times 2^n$ density matrix remains the fundamental bottleneck; we discuss how integrating tensor-network structures can contain the per-iteration cost while preserving reconstruction fidelity. Altogether, these results suggest that physically constrained generative learning offers a scalable and amortizable pathway toward data-driven tomography for noisy intermediate-scale quantum devices.
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