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DTSTAMP:20261027T124936Z
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DESCRIPTION:Foundation neural quantum states are founded in the idea that a
  single neural model should be able to serve multiple Hamiltonians. Thus f
 ar for spin-based systems\, foundation models have fixed an interaction to
 pology (say a spin-chain Ising model) and vary within the parametric space
  of the Hamiltonian\, sometimes for a changing system size. In our recent 
 work\, we show it is possible to have one model train over hundreds of tho
 usands of different Hamiltonians\, changing the interaction topology (e.g.
  from 1D to 2D to arbitrary non-local interactions)\, number of bodies\, a
 nd the weighting of interactions. Our results indicate favorable scaling l
 aws in pretraining\, in which we used contemporary techniques from large l
 anguage models and deep reinforcement learning on systems up to 64 qubits.
  Our deep reinforcement learning algorithm learns the entanglement geometr
 y of systems in pretraining\, finding it to generalize on systems with kno
 wn entangling structures that it never saw in training.  On a held-out gen
 eralisation dataset\, we test our model on unseen systems\, unseen scales\
 , and fine-tune our model on system sizes of 2000 qubits and beyond.\n \nT
 o do this\, we formulate qubit quantum ground-state learning as manifold v
 ariational optimization over centrally odd scalar functions on SU(2)^N. Th
 is replaces explicit Hilbert-space vector amplitudes with manifold functio
 ns on which the Hamiltonian acts through Lie derivatives\, evaluated by cu
 stom automatic differentiation primitives. We prove that the resulting var
 iational principle on this manifold preserves the usual spin-1/2 sector's 
 ground-state upper bound using the Peter-Weyl theorem and justify the choi
 ce of such a representation with a no-go theorem for pure state foundation
  NQS. We then pre-train our foundation model on a dataset of hundreds of t
 housands of different Hamiltonian systems\, varying the connection topolog
 y\, system size\, interaction types and strengths\, bringing together a ce
 ntury of many-body literature. Code for our method\, as well as the model 
 weights are available and open-source. \n\nhttps://arxiv.org/abs/2608.1191
 1 \nhttps://arxiv.org/abs/2609.07591
LOCATION:ETH Zürich\, Hönggerberg HIT E 41.1
ORGANIZER:Tim Heightman
SUMMARY:Foundation Neural Quantum States
URL;VALUE=URI:https://blogs.ethz.ch/lowenergydiscussions/future-talks/
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