Hunting for Hamiltonians with a General-Purpose Symmetry-to-Hamiltonian Approach

Inverse methods that learn models from data are widely used in the field of machine learning to solve difficult engineering tasks. Recently, inverse methods have been applied in the context of quantum physics to engineer quantum models, i.e., Hamiltonians, with targeted properties, such as targeted eigenstates or reduced density matrices. Here we present a new efficient and general-purpose inverse method approach, the symmetric Hamiltonian construction (SHC), for engineering Hamiltonians with particular symmetries, such as integrals of motion or discrete symmetries [1]. This method extends on ideas developed in the slow operator method [2]. Using the SHC inverse method, we design new Hamiltonians with topological properties: superconducting Hamiltonians with Majorana zero modes and Z₂ quantum spin liquid Hamiltonians. In this talk, we will introduce the SHC method and discuss the topological Hamiltonians that we find. Our open-source numerical implementation of the SHC method is available at github.com/ClarkResearchGroup/qosy.

[1] E. Chertkov, B. Villalonga, and B. K. Clark, arXiv:1910.10165 (2019).
[2] H. Kim et al., Phys. Rev. E 92, 012128 (2015).