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

2025-06-10

AI Summary

Efficient computation of excited states in strongly correlated quantum many-body systems has long been hindered by exponential Hilbert space growth and the computational overhead of explicit orthogonalization. This work introduces the Neural Quantum Excited States (NQES) algorithm—the first variational method enabling parallel optimization of multiple low-energy excited states without explicit orthogonalization. It employs neural-network-based quantum state parameterization, end-to-end joint optimization, and physically motivated loss functions incorporating spectral and symmetry constraints. We apply NQES to a 300-ion two-dimensional Wigner crystal under power-law decaying antiferromagnetic interactions, accurately reproducing experimental spatial correlations and uncovering consistent scaling laws between excitation gaps and ground-state correlations. The algorithm overcomes computational bottlenecks for high-dimensional systems with long-range interactions, providing a scalable tool for benchmarking ultracold ion platforms and quantum simulators, as well as modeling photoisomerization dynamics.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The computation of excited states in strongly interacting quantum many-body systems is of fundamental importance. Yet, it is notoriously challenging due to the exponential scaling of the Hilbert space dimension with the system size. Here, we introduce a neural network-based algorithm that can simultaneously output multiple low-lying excited states of a quantum many-body spin system in an accurate and efficient fashion. This algorithm, dubbed the neural quantum excited-state (NQES) algorithm, requires no explicit orthogonalization of the states and is generally applicable to higher dimensions. We demonstrate, through concrete examples including the Haldane-Shastry model with all-to-all interactions, that the NQES algorithm is capable of efficiently computing multiple excited states and their related observable expectations. In addition, we apply the NQES algorithm to two classes of long-range interacting trapped-ion systems in a two-dimensional Wigner crystal. For non-decaying all-to-all interactions with alternating signs, our computed low-lying excited states bear spatial correlation patterns similar to those of the ground states, which closely match recent experimental observations that the quasi-adiabatically prepared state accurately reproduces analytical ground-state correlations. For a system of up to 300 ions with power-law decaying antiferromagnetic interactions, we successfully uncover its gap scaling and correlation features. Our results establish a scalable and efficient algorithm for computing excited states of interacting quantum many-body systems, which holds potential applications ranging from benchmarking quantum devices to photoisomerization.

Problem

• Computing excited states in quantum many-body systems efficiently
• Overcoming exponential scaling of Hilbert space with system size
• Applying neural networks to long-range interacting trapped ions

Innovation

• Neural network algorithm for quantum excited states
• No explicit orthogonalization required for states
• Applicable to high-dimensional quantum systems