# Automatic design of Hamiltonians

## TL;DR

This paper introduces a variational approach to automatically design Hamiltonians by optimizing a loss function based on desired properties, demonstrated on quantum Hall states and aimed at simplifying experimental realization.

## Contribution

It formulates a novel optimization framework for Hamiltonian design using the variational principle, enabling targeted generation and simplification of models for exotic quantum phases.

## Key findings

- Successfully generated Hamiltonians for Moore-Read and Read-Rezayi states.
- Optimized conditions for experimental realization of quantum Hall states.
- Proposed a method to find simpler models for complex quantum phases.

## Abstract

We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties specifying thereby the search query. Using fractional quantum Hall effect as a test system we illustrate how the framework can be used to determine a generating Hamiltonian of a finite-size model wavefunction (Moore-Read Pfaffian and Read-Rezayi states), find optimal conditions for an experiment or "extrapolate" given wavefunctions in a certain universality class from smaller to larger system sizes. We also discuss how the search for approximate generating Hamiltonians may be used to find simpler and more realistic models implementing the given exotic phase of matter by experimentally accessible interaction terms.