两味施温格模型变分量子模拟中可表达性、对称性保护与硬件噪声的分离

中文摘要 AI 辅助

现有的两味施温格模型量子模拟仅在单一晶格尺寸下进行，尚不清楚变分方法能推进到何种程度，以及哪种弱点会首先导致其失效。通过将该模型从N=2推进到6个交错晶格位点，我们发现，在可达尺寸下，限制因素是硬件噪声，而非电路可表达性或可训练性，并确定N=3是现有离子阱实验可立即扩展的可行尺寸。电荷守恒拟设的能量误差坍缩为p/d（变分参数与物理扇区维度之比）的单一函数，并且当p/d升至数量级1时，误差下降超过两个数量级，从而给出L(4N-1) >= binom(2N,N)的可表达性条件（其中L为电路层数）。该条件在化学势上是局部的：在N=3时，零化学势下足够的层数在一阶边界附近留下74.38%的误差，而再增加一层则达到0.08%。电荷守恒还保护了可训练性并防止电荷扇区泄漏：当量子比特数从4翻倍至8时，约束拟设的归一化梯度方差降至其初始值的1/3.56，而无约束电路则为1/13.57。通过比较全局收缩与逐门局部噪声，一个固定参数对照表明，是噪声模型（而非优化器是否在含噪循环内运行）决定了噪声对一阶跃迁的退化程度。在N=4时，无噪声对照达到0.12%的平均误差，而相同电路在1.00%去极化噪声下则达到25.69%至52.81%。

英文摘要

Existing quantum simulations of the two-flavor Schwinger model have run at a single lattice size, and it is not known how far the variational approach can be pushed or which weakness stops it first. Following the model from N = 2 to 6 staggered lattice sites, we find that the binding constraint at reachable sizes is hardware noise rather than circuit expressibility or trainability, and identify N = 3 as the immediately viable extension of existing trapped-ion experiments. The energy error of a charge-conserving ansatz collapses onto one function of p/d, the ratio of variational parameters to physical-sector dimension, and falls by more than two orders of magnitude as p/d rises through order unity, giving the expressibility condition L(4N - 1) >= binom(2N,N) for L circuit layers. The condition is local in chemical potential: at N = 3 the layer count sufficient at zero chemical potential leaves a 74.38% error near the first-order boundary, while one further layer reaches 0.08%. Charge conservation also protects trainability and prevents charge-sector leakage: as the qubit count doubles from 4 to 8, the normalized gradient variance falls to 1/3.56 of its starting value for the constrained ansatz, versus 1/13.57 for an unconstrained circuit. Comparing a global contraction with per-gate local noise, a fixed-parameter control shows that the noise model, not whether the optimizer runs inside the noisy loop, sets how strongly noise degrades the first-order transition. At N = 4, a noiseless control reaches 0.12% mean error, whereas the same circuit at 1.00% depolarizing noise reaches 25.69 to 52.81%.

发表机构

• PES University（PES大学）

机构由 AI 辅助整理，请以论文原文为准。