标题： 量子计算的对称性 显示英文标题

标题： Symmetric quantum computation

摘要： 我们系统地研究了“对称量子电路”这一受限的量子计算模型，该模型基于对称性限制。 这个模型非常适合研究对称性在量子加速中的作用，并且扩展了经典环境中研究的强大对称计算概念。 我们证明，与它们的经典对应物相比，对称量子电路通过高效实现关键的量子子程序（如振幅放大、相位估计以及酉矩阵的线性组合技术）超出了经典电路的能力。 此外，我们考虑了对称态制备任务，并表明它可以在几个有趣且非平凡的情况下被高效执行。 显示英文摘要

摘要： We introduce a systematic study of "symmetric quantum circuits", a restricted model of quantum computation where the restriction is symmetry-based. This model is well-adapted for studying the role of symmetries in quantum speedups, and it extends a powerful notion of symmetric computation studied in the classical setting. We show that symmetric quantum circuits go beyond the capabilities of their classical counterparts by efficiently implementing key quantum subroutines such as amplitude amplification and phase estimation, as well as the linear combination of unitaries technique. In addition, we consider the task of symmetric state preparation and show that it can be performed efficiently in several interesting and nontrivial cases.