链上超对称哈密顿量的零能问题是QMA₁完全问题
Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are $\mathrm{QMA}_1$-Complete
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- Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究科）
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中文总结 AI 辅助
该研究证明了链上超对称哈密顿量的零能问题属于QMA₁完全，通过一维无挫折哈密顿量构造得到基态能量的逆多项式下界，明确了问题的计算复杂性。
中文摘要 AI 辅助
我们研究相互作用排列在一维链上的超对称量子系统的精确零模。对于厄米超荷，判定是否存在零模是QMA₁完全问题，且困难实例在链上是几何局域的。我们还对显式编码的幂零N=2形式进行分类：其精确零问题是QMA₁完全问题，包括关联哈密顿量在链上局域的限制情况。两种分类均采用同时稀疏线性约束的验证定理和相同的一维无挫折哈密顿量构造，该构造为每个归约NO实例的基态能量提供了显式的逆多项式下界，将其与零区分开。
英文摘要
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 $\mathrm{QMA}_1$-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 $\mathrm{QMA}_1$ while allowing cancellations between supercharge terms.
