Differentiable Inverse Design of Two-Body Interactions for the Moore-Read State
Abstract
Designing interactions that stabilize target quantum states is a central challenge in strongly correlated physics. For fractional quantum Hall states, identifying suitable two-body interactions remains difficult even when a target wave function is known. Here we implement a differentiable inverse-design approach that combines automatic differentiation with exact diagonalization to optimize two-body interactions, using the Moore--Read Pfaffian state as a benchmark. The optimized ground states achieve overlaps exceeding 99\% with the target for systems containing up to 12 electrons. Excitation and entanglement spectra provide complementary finite-size diagnostics. A common exponential pseudopotential profile retains an overlap of 91.1\% at 14 electrons without further optimization, supporting its transferability beyond the optimization sizes. These results demonstrate the approach on a non-Abelian quantum Hall benchmark and motivate its application to other numerically accessible trial states for which suitable approximate parent Hamiltonians remain unknown.
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BibTeX
@misc{yang2026differentiable,
title = {{Differentiable Inverse Design of Two-Body Interactions for the Moore-Read State}},
author = {Yi Yang and Xin Wan and Zi-Xiang Hu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.23695},
eprint = {2607.23695},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23695},
}
RIS
TY - UNPB
TI - Differentiable Inverse Design of Two-Body Interactions for the Moore-Read State
AU - Yi Yang
AU - Xin Wan
AU - Zi-Xiang Hu
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2607.23695
UR - https://arxiv.org/abs/2607.23695
AB - Designing interactions that stabilize target quantum states is a central challenge in strongly correlated physics. For fractional quantum Hall states, identifying suitable two-body interactions remains difficult even when a target wave function is known. Here we implement a differentiable inverse-design approach that combines automatic differentiation with exact diagonalization to optimize two-body interactions, using the Moore--Read Pfaffian state as a benchmark. The optimized ground states achieve overlaps exceeding 99\% with the target for systems containing up to 12 electrons. Excitation and entanglement spectra provide complementary finite-size diagnostics. A common exponential pseudopotential profile retains an overlap of 91.1\% at 14 electrons without further optimization, supporting its transferability beyond the optimization sizes. These results demonstrate the approach on a non-Abelian quantum Hall benchmark and motivate its application to other numerically accessible trial states for which suitable approximate parent Hamiltonians remain unknown.
ER -