Inverse Hamiltonian design of highly-entangled quantum many-body systems

Solving inverse problems to identify Hamiltonians with desired properties is promising for the discovery of new principles. In quantum many-body systems, quantum entanglement plays a pivotal role in not only the characterization of quantum matter but also future quantum computing. However, an efficient way to create Hamiltonians exhibiting large quantum entanglement remains unclear. Here, we apply the inverse design framework using automatic differentiation [1] to quantum many-body systems to create Hamiltonians with large quantum entanglement. Our method can automatically construct the Kitaev spin models on both honeycomb and square-octagon lattices, whose ground states are exactly shown to be quantum spin liquids [2,3]. On triangular and maple-leaf lattices with geometrical frustration, we find spatially inhomogeneous models, while we can derive a symmetric model on the maple-leaf case. We demonstrate that anisotropic interactions contribute to enhancing quantum entanglement. The method can be combined with numerical methods such as tensor networks, paving the way for the automatic design of new quantum systems.

[1] K. Inui and Y. Motome, Commun. Phys. 6, 37 (2023). [2] A. Kitaev, Ann. Phys. 321, 2 (2006). [3] S. Yang et. al., Phys. Rev. B 76, 180404 (2007).