Adaptive-basis sample-based neural diagonalization for quantum many-body systems

Estimating ground-state energies of quantum many-body systems is challenging due to the exponential growth of Hilbert space. Sample-based diagonalization (SBD) addresses this by projecting the Hamiltonian onto a subspace of selected basis configurations but works only for concentrated ground-state wave functions. We propose two neural network-enhanced SBD methods: sample-based neural diagonalization (SND) and adaptive-basis SND (AB-SND). Both leverage autoregressive neural networks for efficient sampling; AB-SND also optimizes a basis transformation to concentrate the wave function. We explore classically tractable single- and two-spin rotations, and more expressive unitaries implementable on quantum computers. On quantum Ising models, SND performs well for concentrated states, while AB-SND consistently outperforms SND and standard SBD in less concentrated regimes.