Hamiltonian Learning from Time Dynamics Using Variational Algorithms.

Area of Science:

• Quantum Physics
• Quantum Computing
• Machine Learning

Background:

• The Hamiltonian governs quantum system dynamics via the Schrödinger equation.
• Accurate Hamiltonian reconstruction is crucial for quantum simulations and control.
• Existing methods often rely on specific Hamiltonian structures, limiting their applicability.

Purpose of the Study:

• To develop a general and efficient method for reconstructing quantum Hamiltonians from time-series data.
• To extend the developed protocol for quantum state learning using observable time-series data.
• To demonstrate the method's efficacy on various Hamiltonians, including XX, ZZ couplings, and SU(3) generators.

Main Methods:

• Reconstructing the Hamiltonian in the Pauli basis using measurements on random quantum states.
• Implementing time propagation via Trotterization with variational optimization and gradient computation on quantum circuits.
• Validating the reconstructed Hamiltonian by predicting dynamics of unseen observables and states.

Main Results:

• Successfully reconstructed Hamiltonians and reproduced dynamics of unseen observables.
• Extended the protocol to perform quantum state learning by solving the inverse problem.
• Demonstrated results on XX, ZZ couplings, and transverse-field Ising Hamiltonians, proposing a method for SU(3) group generators.

Conclusions:

• The proposed Hamiltonian learning scheme is general, efficient, and flexible regarding observables and initial states.
• This work paves the way for utilizing Hamiltonian learning in quantum machine learning for time-series prediction.
• The method offers a significant advancement in quantum system characterization and learning.