半自治近似量子本征解的强化学习
Reinforcement learning for semi-autonomous approximate quantum eigensolver
摘要：
利用算符的本征矢和本征值来刻画算符，可以知道算符对任何量子态的作用。在这里，我们提出了一个协议，以获得任意厄米量子算符的本征向量的近似。该协议基于测量和反馈过程，这是强化学习协议的特征。我们的方案由两个系统组成，一个名为环境的黑盒子和一个名为主体的量子态。环境的作用是通过酉矩阵$\hat{U}_E=e^{-iτ\hat{\mathcal{O}}_E}$改变任何量子态，其中$\hat{\mathcal{O}}_E$是厄米算符，而$τ$是实参数。智能体是一种量子态，它通过与环境的重复交互、反馈过程和半随机旋转来适应$\hat{\mathcal{O}}_E$的某些特征向量。利用该方法，我们可以在10次迭代以内得到平均保真度超过90%的随机量子比特算符本征向量的近似，在300次迭代以内得到平均保真度超过98%的随机量子比特算符本征向量的近似.此外，对于双量子比特情形，对于随机算符，在8000次迭代中得到的四个本征矢量的量子数均在89%以上，对于以Bell态为本征矢量的算符，量子数均为$99\%$.该协议可以用于实现半自主量子设备，这些设备应该能够以最少的资源提取信息并做出决定，而无需人工干预。
英文摘要：
The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrix $\hat{U}_E=e^{-iτ\hat{\mathcal{O}}_E}$ where $\hat{\mathcal{O}}_E$ is a Hermitian operator, and $τ$ is a real parameter. The agent is a quantum state which adapts to some eigenvector of $\hat{\mathcal{O}}_E$ by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90\% in less than 10 iterations, and surpass 98\% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89\% in 8000 iterations for a random operator, and fidelities of $99\%$ for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
