Powerful wave function ansätze have powered advances in finding ground state representations, reconstructing quantum states from data, and modelling dynamics in quantum many-body systems. While recurrent neural networks (RNNs) are computationally efficient, the recurrent nature can limit their capacity to capture long-range correlations. Transformer models with their underlying self-attention mechanism excel at capturing these long-range correlations, but incur increased computational requirements, restricting applications to small physical systems. Researchers explored the multi-layer perceptron (MLP) mixer model as a wave function ansatz to address these limitations by mixing inform.

MLP Transformers Enable Scalable Quantum System Simulations

Researchers at University of Ottawa achieved a fivefold speedup in simulating large quantum systems by combining their new multi-layer perceptron (MLP) mixer with transformer models. Previously, simulations exceeding approximately twenty particles were computationally prohibitive due to limitations within recurrent neural networks and standard transformers. The hierarchical architecture overcomes existing bottlenecks by efficiently capturing both short- and long-range entanglement, important for accurately representing complex quantum states, while maintaining computational feasibility on larger scales than was possible before.

By employing this novel wave function ansatz, the researchers demonstrated competitive performance against state-of-the-art methods when finding ground state representations across various phases of matter, paving the way for investigations into more intricate quantum phenomena. The University of Ottawa team’s new approach achieved simulations involving up to 20 particles; a significant improvement over prior limits where recurrent neural networks struggled beyond approximately twenty due to their inability to represent long-range entanglement, crucial for complex quantum states.

Specifically, applying it to two-dimensional transversefield Ising models and arrays of Rydberg atoms, both used as testbeds, the MLP mixer outperformed standard RNNs and transformers at larger system sizes despite all three architectures employing ‘patched input arrangements’, grouping individual particle data together. Representational accuracy was also assessed alongside computational efficiency across different phases of matter near points of quantum phase transition; while RNNs proved most efficient with smaller systems, this architecture demonstrated superior scaling capabilities.

Scalability advances trade off potential accuracy losses from patch-based input representation

While demonstrably improving scalability beyond what was previously possible with recurrent networks or transformers, an important tension remains regarding input definitions: performance is currently tied to specific ways data representing quantum particles are arranged as ‘patches’. This reliance introduces complexity and raises questions about whether these gains come at the cost of information loss compared to single-site representations used by other approaches.

The team acknowledges that relying on ‘patches’ may introduce such limitations; however, it still represents a strong step forward nonetheless. It successfully competes with existing state-of-the-art models like RNNs and transformers, particularly at larger scales where those struggle due to computational demands.

This hybrid approach combining MLP mixers with transformer technology unlocks new possibilities for exploring complex quantum systems despite input limitations. Next steps involve adapting these architectures to tackle even more complex scenarios and broaden their applicability across diverse physical settings here. This resulting wave function ansatz promises investigations into more intricate phases of matter by providing access to larger, more realistic system sizes than were formerly possible.

The researchers demonstrated that a multi-layer perceptron (MLP) mixer model can represent the ground state of two-dimensional quantum many-body systems, like transversefield Ising models and arrays of Rydberg atoms, with improved scalability compared to recurrent neural networks and transformers. While performance currently depends on grouping particle data as “patches,” this approach allows for calculations with larger system sizes where other methods become computationally limited.

The MLP mixer achieved better scaling capabilities while maintaining representational accuracy across different phases of matter; future work will focus on adapting these architectures to more complex physical scenarios. This offers access to simulations of increasingly intricate quantum systems.

👉 More information
🗞 Scalable Neural Wave Functions via Information Mixing and Hierarchical Network Architectures
✍️ Faith Oyedemi and Stefanie Czischek (University of Ottawa)
🧠 ArXiv: https://arxiv.org/abs/2610.30257

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