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Resetting Uncontrolled Quantum Systems

机译：重置不受控制的量子系统

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摘要

We consider a scenario where we wish to bring a closed system of known Hilbert space dimension d S (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time t 0 . The target is out of our control: This means that we ignore both its free Hamiltonian and how the system interacts with other quantum systems we may use to influence it. Under these conditions, we prove that there exist protocols within the framework of nonrelativistic quantum physics that reset the target system to its exact quantum state at t 0 . Each “resetting protocol” is successful with nonzero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure. When the target is a qubit and the interaction is sampled from the Haar measure, the simplest resetting circuits have a significant average probability of success and their implementation is within reach of current quantum technologies. Finally, we find that, in case the resetting protocol fails, it is possible to run a further protocol that, if successful, undoes both the natural evolution of the target and the effects of the failed protocol over the latter. By chaining in this fashion several such protocols, one can substantially increase the overall probability of a successful resetting.
机译：我们考虑了一个方案，我们希望在过去时间t 0返回其未知的Hilbert Space Dimension D S（目标）的封闭系统，而不是未知的Hamiltonian演变，返回其量子状态T 0。目标是脱离我们的控制：这意味着我们忽略了其自由的汉密尔顿人以及系统如何与其他量子系统互动，我们可以使用它来影响它。在这些条件下，我们证明存在在非素描量子物理框架内存在协议，其在T 0将目标系统重置为其精确量子状态。每个“重置协议”是成功的，对所有可能的免费Hamiltonians和交互统一的非零概率，保存零测量的子集。当目标是qubit并且从哈尔测量采样交互时，最简单的重置电路具有超大平均成功概率，其实现在电流量子技术范围内。最后，我们发现，如果重置协议失败，则可以运行另一个协议，如果成功，则撤消目标的自然演进以及失败协议在后者上的影响。通过在这种方式中链接几个这样的协议，可以大大增加成功重置的总体概率。

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