Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are QMA1-Complete
Abstract
We determine the computational complexity of deciding whether a supersymmetric quantum system on a one-dimensional chain has a zero-energy ground state. We prove QMA1-completeness for two input models, formulated in terms of Hermitian and nilpotent supercharges, respectively. In the Hermitian model, both the supercharge terms and the Hamiltonian have bounded range on the chain; in the nilpotent model, this geometric restriction applies only to the Hamiltonian. The hardness reduction from quantum satisfiability on a chain preserves exact zero energy and gives an inverse-polynomial ground-energy lower bound for negative instances. A common verification method establishes membership in QMA1 while allowing cancellations between supercharge terms.
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BibTeX
@misc{wang2026zeroenergy,
title = {{Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are $\mathrmQMA_1$-Complete}},
author = {Yibin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.29333},
eprint = {2608.29333},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29333},
}
RIS
TY - UNPB
TI - Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are QMA_1-Complete
AU - Yibin Wang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2608.29333
UR - https://arxiv.org/abs/2608.29333
AB - We determine the computational complexity of deciding whether a supersymmetric quantum system on a one-dimensional chain has a zero-energy ground state. We prove QMA_1-completeness for two input models, formulated in terms of Hermitian and nilpotent supercharges, respectively. In the Hermitian model, both the supercharge terms and the Hamiltonian have bounded range on the chain; in the nilpotent model, this geometric restriction applies only to the Hamiltonian. The hardness reduction from quantum satisfiability on a chain preserves exact zero energy and gives an inverse-polynomial ground-energy lower bound for negative instances. A common verification method establishes membership in QMA_1 while allowing cancellations between supercharge terms.
ER -