标题： 多项式效率的量子增强变分蒙特卡洛方法在物理化学应用中训练神经网络量子态 显示英文标题

标题： Polynomially efficient quantum enabled variational Monte Carlo for training neural-network quantum states for physico-chemical applications

摘要： 神经网络量子态（NQS）为模拟物理系统提供了一种灵活且表达能力强的替代传统变分假设的方法。 基于能量框架，如Hopfield网络和受限玻尔兹曼机，利用统计物理学将量子态映射到能量景观上，作为记忆描述符。 在这里，我们展示出这些模型可以使用由量子设备增强的蒙特卡洛技术高效训练。 我们的算法随着电路宽度和深度线性扩展，需要恒定的测量次数，避免了电路中间的测量，并且在存储上是多项式的，确保了最优效率。 它适用于相位场和振幅场，与先前的方法相比显著扩大了试验空间。 量子辅助采样加速了马尔可夫链的收敛并提高了样本保真度，相较于经典方法具有优势。 我们通过准确学习局部自旋模型和非局域电子结构哈密顿量的基态来验证我们的方法，即使在具有强多参考关联的畸变分子几何中也是如此。 基准比较显示与传统方法有稳健的一致性。 这项工作强调了结合机器学习协议与近程量子设备用于量子态学习的潜力，具有理论化学和凝聚态物理中的应用前景。 显示英文摘要

摘要： Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines, leverage statistical physics to map quantum states onto an energy landscape, functioning as memory descriptors. Here, we show that such models can be efficiently trained using Monte Carlo techniques enhanced by quantum devices. Our algorithm scales linearly with circuit width and depth, requires constant measurements, avoids mid-circuit measurements, and is polynomial in storage, ensuring optimal efficiency. It applies to both phase and amplitude fields, significantly expanding the trial space compared to prior methods. Quantum-assisted sampling accelerates Markov Chain convergence and improves sample fidelity, offering advantages over classical approaches. We validate our method by accurately learning ground states of local spin models and non-local electronic structure Hamiltonians, even in distorted molecular geometries with strong multi-reference correlations. Benchmark comparisons show robust agreement with traditional methods. This work highlights the potential of combining machine learning protocols with near-term quantum devices for quantum state learning, with promising applications in theoretical chemistry and condensed matter physics.