使用 Classical Shadows 恢复量子计算中的对称性
Restoring symmetries in quantum computing using Classical Shadows
AI总结：
本文提出利用 Classical Shadow 后处理对量子试探波函数施加宇称、粒子数和自旋等对称性，无需量子投影，并经去随机化优化后可高效预测对称恢复态可观测量。
摘要：
我们提出一种方法，可从量子计算机上制备的、可能不满足某些对称性的试探波函数出发，强制施加这些对称性。该技术无需在量子计算机本身执行投影；相反，这一任务作为对系统“Classical Shadow（经典影子）”的后处理步骤完成。文中针对在相互作用多体系统中尤为重要的宇称、粒子数和自旋投影算符给出了方法示例。我们将该方法与另一种基于对量子寄存器直接测量的经典后处理技术进行比较。结果表明，一旦采用去随机化进行优化，本方案在预测对称性恢复态上的可观测量时可具有竞争力。该技术还通过应用于计算配对模型哈密顿量的投影能量得到说明。
英文摘要：
We introduce a method to enforce some symmetries starting from a trial wave-function prepared on quantum computers that might not respect these symmetries. The technique eliminates the necessity for performing the projection on the quantum computer itself. Instead, this task is conducted as a post-processing step on the system's "Classical Shadow". Illustrations of the approach are given for the parity, particle number, and spin projectors that are of particular interest in interacting many-body systems. We compare the method with another classical post-processing technique based on direct measurements of the quantum register. We show that the present scheme can be competitive to predict observables on symmetry-restored states once optimization through derandomization is employed. The technique is illustrated through its application to compute the projected energy for the pairing model Hamiltonian.
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