Solving excited states for long-range interacting trapped ions with neural networks

Area of Science:

• Quantum Many-Body Physics
• Computational Quantum Chemistry

Background:

• Calculating excited states in strongly interacting quantum systems is crucial but computationally demanding.
• The exponential scaling of Hilbert space with system size poses a significant challenge.

Purpose of the Study:

• To develop a scalable algorithm for accurately and efficiently computing multiple low-lying excited states in large quantum systems.
• To demonstrate the algorithm's applicability to various models, including the Haldane-Shastry model and trapped-ion systems.

Main Methods:

• Building upon the natural-excited-states (NES) framework.
• Implementing a scalable algorithm for spin systems with long-range interactions.
• Applying the framework to Haldane-Shastry model and trapped-ion systems in a Wigner crystal.

Main Results:

• The algorithm efficiently computes multiple excited states and their observable expectation values.
• Computed excited states for trapped-ion systems show spatial correlations similar to ground states.
• Gap scaling and correlation features were successfully uncovered for antiferromagnetic interacting ion systems.

Conclusions:

• A scalable and efficient algorithm for computing excited states in interacting quantum many-body systems has been established.
• The method offers potential applications in benchmarking quantum devices and studying phenomena like photoisomerization.