AI 中文总结
该研究提出从量子可观测量动力学学习未知量子酉的变分算法，无结构假设。通过硬件高效电路和经典后处理学习演化算子与哈密顿量，经三个实验验证通用性，在不同条件下取得高精度结果，为量子计算相关研究提供新方法。
AI 中文摘要
我们提出了一种变分算法，用于从时间序列可观测量测量中学习未知量子酉，且对目标无结构假设。核心分离在于：一个硬件高效的参数化电路通过可观测量匹配学习演化算子U；当目标为exp(-iH*tau)时，通过矩阵对数进行经典后处理实现哈密顿量识别。三个实验证明了该方法的通用性。实验结果包括无噪声时MSE达1.61e-14，能精确恢复哈密顿量系数；能拟合多种门且不依赖特罗特化结构；在有噪声情况下能以低于8%的误差恢复伊辛哈密顿量项。
英文摘要
We present a variational algorithm for learning an unknown quantum unitary from time-series observable measurements, with no structural assumption about the target. The core separation: a hardware-efficient parametrised circuit learns the evolution operator U via observable matching; Hamiltonian identification follows as classical post-processing via matrix logarithm, when the target happens to be exp(-iH*tau). Three experiments establish the method's generality. First, a noiseless proof of correctness with exact gradients (L-BFGS-B) achieves MSE 1.61e-14 and recovers all Hamiltonian coefficients to six decimal places. Second, a gate-learning experiment fits CNOT, iSWAP, and a Haar-random SU(4) element -- none generated by any fixed Hamiltonian -- all to process fidelity 1.000000, confirming the method does not rely on Trotterisation structure. Third, quantum deployment via SPSA-Adam under Qiskit Aer depolarising noise (p1=0.001, p2=0.01, Nshots=1024) recovers all three Ising Hamiltonian terms with errors below 8%. The optimiser, SPSA-Adam, combines SPSA's hardware-efficient two-point gradient estimation with Adam's adaptive moment updates. A four-stage moment-warm curriculum progressively extends the training horizon, converting a global non-convex problem into a sequence of well-posed local ones.
Comments7 pages, 15 tables, 1 algorithm.This preprint is based on and extends the author's Master's thesis completed at Université Ferhat Abbas Sétif 1 (2026)
