We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean square error ϵ using \({\mathcal{O}}(1/\epsilon )\) total evolution time, which is independent of the system size, in a way that is robust against state-preparation and measurement error. In the protocol, we only use bosonic coherent states, beam splitters, phase shifters, and homodyne measurements, which are easy to implement on many experimental platforms. A key technique we develop is to apply random unitaries to enforce symmetry in the effective Hamiltonian, which may be of independent interest.

我们开发了一种协议，用于从具有海森堡有限标度的动力学中学习一类相互作用的玻色哈密顿量。对于具有底层有界度图结构的哈密顿量，我们可以使用\({\mathcal{O}}(1/\epsilon )\)总演化时间来学习具有均方根误差ϵ的所有参数，该时间与系统无关大小，以一种对状态准备和测量误差具有鲁棒性的方式。在协议中，我们只使用玻色相干态、分束器、移相器和零差测量，这些很容易在许多实验平台上实现。我们开发的一项关键技术是应用随机酉来强制有效哈密顿量的对称性，这可能是独立的兴趣。