Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates

Area of Science:

• Quantum physics
• Machine learning
• Inverse problems

Background:

• Reconstructing system Hamiltonians from measurements is a key challenge in quantum physics.
• Previous work showed generic many-body local Hamiltonians can be recovered without correlation function values.

Purpose of the Study:

• To explore Hamiltonian reconstruction for various quantum systems.
• To apply supervised learning, specifically neural networks, to solve this inverse problem.
• To address challenges posed by middle-lying eigenstates.

Main Methods:

• Utilized supervised learning via neural networks for Hamiltonian reconstruction.
• Applied neural networks to low-lying eigenstates, finding them efficient and scalable.
• Developed a modified transfer learning method for ill-posed problems involving middle-lying eigenstates.
• Employed neural networks to generate initial points for BFGS numerical optimization.

Main Results:

• Neural networks proved efficient and scalable for reconstructing Hamiltonians of low-lying eigenstates, even with limited data.
• A transfer learning approach was successfully adapted for ill-posed inverse problems concerning middle-lying eigenstates.
• Neural networks effectively provided initial points for BFGS optimization, improving numerical efficiency.

Conclusions:

• Neural networks offer a powerful and scalable solution for reconstructing quantum system Hamiltonians.
• Transfer learning provides a viable strategy for tackling complex inverse problems in quantum physics.
• This work advances the application of machine learning in solving fundamental problems in quantum mechanics.