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

Abstract: Accurately estimating ground-state energies of quantum many-body systems is still a challenging computational task because of the exponential growth of the Hilbert space with the system size. Sample-based diagonalization (SBD) methods address this problem by projecting the Hamiltonian onto a subspace spanned by a selected set of basis configurations. In this article, we introduce two neural network-enhanced approaches for SBD: sample-based neural diagonalization (SND) and adaptive-basis SND (AB-SND). Both employ autoregressive neural networks to efficiently sample relevant basis configurations, with AB-SND additionally optimizing a parameterized basis transformation so that the ground-state wave function becomes more concentrated. We consider different classes of basis transformations: single-spin and non-overlapping two-spin rotations, which are tractable on classical computers, and also more expressive global unitaries that can be implemented using quantum circuits. We demonstrate the effectiveness of these techniques on various quantum Ising models, showing that SND achieves high accuracy for concentrated ground states, while AB-SND consistently outperforms both SND and more conventional SBD methods, allowing entering regimes in which the ground state is not concentrated in the original computational basis.