标题： 是否打破：自适应量子模拟中的对称性，施温格模型的一个案例研究 显示英文标题

标题： To break, or not to break: Symmetries in adaptive quantum simulations, a case study on the Schwinger model

摘要： 我们研究对称性在构建自适应变分量子本征求解器的资源高效算子池中的作用。 特别是，我们关注晶格施温格模型，这是一个 $1+1$ 维电动力学的离散化模型，我们将其用作具有连续极限的自旋链的代理。 我们进行了大量模拟，包括总共 $11$ 种不同的算子池，这些算子池系统地且独立地打破或保持离散平移、电荷（磁化）守恒以及激发的费米子局域性的组合。 电路深度是当前量子硬件的主要瓶颈，我们发现近期最有效的参数形式是由那些 $\textit{break}$ 平移不变性、守恒电荷并导致浅层电路的算子池获得的。 另一方面，我们预计在未来的纠错量子设备中，测量次数将成为限制因素；我们的研究结果表明，那些 $\textit{preserving}$ 平移不变性的算子池可能更适合此类平台。 显示英文摘要

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 ans\"atze 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.