Implications of the PXP ground-state sign structure for neural-network variational Monte Carlo
Abstract
Positive-definite neural-network quantum states cannot directly represent the ground state of the PXP Hamiltonian, since the ground-state wavefunction carries a nontrivial relative-sign structure. Building on the chiral symmetry of the PXP Hamiltonian, we show that this sign structure is fixed exactly by the parity of the total up-spin number: a diagonal unitary transformation that assigns a sign to each spin configuration according to this parity maps the PXP Hamiltonian to its negative, rendering the transformed Hamiltonian stoquastic on the Rydberg-blockaded Hilbert space. Since the configuration graph of allowed configurations is connected, the Perron-Frobenius theorem guarantees a unique, strictly positive ground state of the transformed Hamiltonian, yielding an exact sign rule for the ground state of the original Hamiltonian in terms of the parity of the up-spin number. Variational Monte Carlo performed directly on the transformed Hamiltonian with a positive-definite ansatz therefore requires no architecture-specific modification to represent the true ground state. We evaluate the performance of this formulation using five representative neural-network quantum state architectures, SineKAN, reflection-symmetrized SineKAN, RBM, MLP, and LSTM, for different chain lengths.
Related
- A Boson-informed neural network for Ground States of Many-Body Schrödinger equations
- INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities
- Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization
- Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Kohn--Sham method
- Landscape of pentaquark bound states with neural-network Variational Monte Carlo
BibTeX
@misc{park2026implications,
title = {{Implications of the PXP ground-state sign structure for neural-network variational Monte Carlo}},
author = {Jun Sur Richard Park and Kwangmin Yu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00603},
eprint = {2611.00603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00603},
}
RIS
TY - UNPB
TI - Implications of the PXP ground-state sign structure for neural-network variational Monte Carlo
AU - Jun Sur Richard Park
AU - Kwangmin Yu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00603
UR - https://arxiv.org/abs/2611.00603
AB - Positive-definite neural-network quantum states cannot directly represent the ground state of the PXP Hamiltonian, since the ground-state wavefunction carries a nontrivial relative-sign structure. Building on the chiral symmetry of the PXP Hamiltonian, we show that this sign structure is fixed exactly by the parity of the total up-spin number: a diagonal unitary transformation that assigns a sign to each spin configuration according to this parity maps the PXP Hamiltonian to its negative, rendering the transformed Hamiltonian stoquastic on the Rydberg-blockaded Hilbert space. Since the configuration graph of allowed configurations is connected, the Perron-Frobenius theorem guarantees a unique, strictly positive ground state of the transformed Hamiltonian, yielding an exact sign rule for the ground state of the original Hamiltonian in terms of the parity of the up-spin number. Variational Monte Carlo performed directly on the transformed Hamiltonian with a positive-definite ansatz therefore requires no architecture-specific modification to represent the true ground state. We evaluate the performance of this formulation using five representative neural-network quantum state architectures, SineKAN, reflection-symmetrized SineKAN, RBM, MLP, and LSTM, for different chain lengths.
ER -