破缺与否：自适应量子模拟中的对称性——以Schwinger模型为例的案例研究
To break, or not to break: Symmetries in adaptive quantum simulations, a case study on the Schwinger model
AI总结：
该研究以格点Schwinger模型为对象，探究对称性对自适应变分量子本征求解器算符池效率的影响，发现浅电路需求下破缺平移不变性的算符池更优，而未来纠错量子器件中保留平移不变性的算符池更具前景。
摘要：
我们研究了对称性在为自适应变分量子本征求解器构建资源高效的算符池时的作用。具体而言，我们聚焦于格点Schwinger模型——一种1+1维电动力学的离散化模型，我们将其作为具有连续极限的自旋链的代理模型。我们开展了大量模拟，共涉及11种不同的算符池，这些算符池均系统且独立地破缺或保留离散平移、电荷（磁化强度）守恒以及激发的费米子局域性的组合特性。电路深度是当前量子硬件的主要瓶颈，我们发现，近期内最高效的拟设由破缺平移不变性、守恒电荷且能生成浅电路的算符池得到。另一方面，我们预计采样数将成为未来纠错量子器件的限制因素；我们的研究结果表明，保留平移不变性的算符池可能更适合此类平台。
英文摘要：
We investigate the role of symmetries in constructing resource-efficient operator pools for adaptive variational quantum eigensolvers. In particular, we focus on the lattice Schwinger model, a discretized model of $1+1$ dimensional electrodynamics, which we use as a proxy for spin chains with a continuum limit. We present an extensive set of simulations comprising a total of $11$ different operator pools, which all systematically and independently break or preserve a combination of discrete translations, the conservation of charge (magnetization) and the fermionic locality of the excitations. Circuit depths are the primary bottleneck in current quantum hardware, and we find that the most efficient ansätze in the near-term are obtained by pools that $\textit{break}$ translation invariance, conserve charge, and lead to shallow circuits. On the other hand, we anticipate the shot counts to be the limiting factor in future, error-corrected quantum devices; our findings suggest that pools $\textit{preserving}$ translation invariance could be preferable for such platforms.
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