施温格模型的对称性约束量子误差缓解
Symmetry Constrained Quantum Error Mitigation for the Schwinger Model
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中文总结 AI 辅助
该研究针对施温格模型，探索两种量子模拟设置下的对称性约束量子误差缓解，发现后选择可消除60%噪声误差，VQE中对称性验证仅降低基态能量偏差，为格点规范理论模拟提供实用指导。
中文摘要 AI 辅助
量子误差缓解（QEM）是近期量子模拟的核心，格点规范理论也不例外，其物理对称性为噪声量子态提供了天然的一致性检验。本工作研究了去极化噪声下的规范理论——（1+1）维施温格模型的宇称和费米子数对称性，以及数字量子模拟下的对称性验证。我们考察了两种设置：第一种是绝热态制备中的对称区后选择，随后对手征凝聚进行实时测量；第二种是变分量子本征求解器（VQE）框架内的对称性验证。在第一种设置中，后选择可降低手征凝聚的偏差，持续消除系统中高达60%的量子噪声诱导误差。受低噪声 regime 下观测到的剩余偏差规律性的启发，我们进一步引入了一种全局噪声校准方法，该方法从经典可处理的小格点获取，并应用于大格点，可在统计不确定度内恢复无噪声的手征凝聚值。然而在VQE中，对称性验证似乎并不能普遍改善优化参数或制备态的保真度，尽管它降低了估计基态能量的偏差。这表明，改进变分算法中的噪声代价函数估计器并不一定能提升算法的结果。我们的结果展示了对称性验证在不同方法中的优势，同时确定其效用关键取决于它在计算流程中的应用位置，为格点规范理论量子模拟中对称性辅助的量子误差缓解提供了实用指导。
英文摘要
Quantum error mitigation (QEM) is at the very heart of near-term quantum simulations and lattice gauge theories are no exceptions, rather their physical symmetries provide natural consistency checks on noise quantum states. In this work, we exploit the parity and fermion-number symmetries of a gauge theory, the (1+1)-dimensional Schwinger model, under depolarising noise and investigate symmetry verification under digital quantum simulation. We investigate two set-ups - symmetry- sector post-selection in adiabatic state preparation followed by real-time measurements of the chiral condensate and symmetry verification within a variational quantum eigensolver (VQE). In the first case, post-selection reduces the bias in the chiral condensate consistently removing up to 60% of the quantum noise induced error in our system. Motivated by the observed regularity of the residual bias (in the low-noise regime), we further introduce a global-noise calibration obtained from classically accessible smaller lattices and implemented on larger lattices recovering noiseless chiral condensate values within statistical uncertainty. However, in VQE, symmetry verification does not seem to generally improve the optimised parameters or the fidelity of the prepared states, although it reduces the bias in the estimated ground-state energy. This demonstates that improving a noisy cost-function estimator in variational algorithms does not necessarily improve the outcome of the algorithm. Our results show the strength of symmetry verification in different approaches while establishing that its usefulness critically depends on where it is applied in the computational workflow, and provide practical guidance for symmetry-assisted quantum error mitigation in quantum simulations of lattice gauge theories.
