Speakers
Description
We formulate $\text{spin-}1/2$ quantum ground-state learning as manifold variational optimization over centrally odd scalar
functions on $\mathrm{SU}(2)^N$. This replaces explicit Hilbert-space
vector amplitudes with manifold functions acted on by Lie-derivative
Hamiltonians via automatic differentiation. We prove a novel variational principle in this function-space that preserves the $\text{spin-}1/2$ manifold
variational principle, then train our foundation model on hundreds of thousands of different Hamiltonian systems, varying the connection topology, system size, and edge weights, bringing together 100 years of many-body literature to construct our own training datasets. We construct a state-of-the-art sampling scheme for $\mathrm{SU}(2)$ replica-exchange Langevin sampling and sharded natural-gradient optimization, extending the KFAC optimizer to rank-four tensors in order to efficiently train the model on small systems. Our foundation model then generalises to unseen Hamiltonian system topologies and unseen system scales up to $100+$ qubits. Preprint in preparation in which will open-source code and model weights.
| Topic | Tensor methods and quantum-inspired machine learning |
|---|---|
| Additional Topic | Theoretical foundations of quantum learning |