Wanjura Clara C, Marquardt Florian
Max Planck Institute for the Science of Light, Erlangen, Germany.
Department of Physics, University of Erlangen-Nuremberg, Erlangen, Germany.
Nat Commun. 2025 Jul 17;16(1):6595. doi: 10.1038/s41467-025-61665-6.
The widespread adoption of machine learning and artificial intelligence in all branches of science and technology creates a need for energy-efficient, alternative hardware. While such neuromorphic systems have been demonstrated in a wide range of platforms, it remains an open challenge to find efficient and general physics-based training approaches. Equilibrium propagation (EP), the most widely studied approach, has been introduced for classical energy-based models relaxing to an equilibrium. Here, we show a direct connection between EP and Onsager reciprocity and exploit this to derive a quantum version of EP. For an arbitrary quantum system, this can now be used to extract training gradients with respect to all tuneable parameters via a single linear response experiment. We illustrate this new concept in examples in which the input or the task is of quantum-mechanical nature, e.g., the recognition of many-body ground states, phase discovery, sensing, and phase boundary exploration. Quantum EP may be used to solve challenges such as quantum phase discovery for Hamiltonians which are classically hard to simulate or even partially unknown. Our scheme is relevant for a variety of quantum simulation platforms such as ion chains, superconducting circuits, Rydberg atom tweezer arrays and ultracold atoms in optical lattices.
机器学习和人工智能在所有科学技术分支中的广泛应用，引发了对节能型替代硬件的需求。虽然这种神经形态系统已在广泛的平台上得到展示，但找到高效且通用的基于物理的训练方法仍然是一个悬而未决的挑战。平衡传播（EP）是研究最广泛的方法，它已被引入用于使经典的基于能量的模型松弛到平衡状态。在这里，我们展示了EP与昂萨格互易性之间的直接联系，并利用这一点推导出EP的量子版本。对于任意量子系统，现在可以通过单个线性响应实验来提取关于所有可调参数的训练梯度。我们在输入或任务具有量子力学性质的示例中说明了这一新概念，例如多体基态的识别、相位发现、传感和相界探索。量子EP可用于解决诸如哈密顿量的量子相位发现等挑战，这些哈密顿量在经典情况下难以模拟甚至部分未知。我们的方案适用于各种量子模拟平台，如离子链、超导电路、里德堡原子镊子阵列和光学晶格中的超冷原子。
