通过高阶量子操作对间接量子控制方案进行基准测试

中文摘要 AI 辅助

间接量子控制旨在通过对辅助控制器进行干预来操纵目标系统，该辅助控制器与目标系统相互作用。我们使用高阶量子操作的语言来制定有限步间接控制协议，将可允许的控制器操作表示为确定性超仪器。这种表示将不受控制的固定动力学与可控操作分离开来，并允许将最优控制问题写为针对所选品质因数的半定规划。由此产生的最优值通过提供有限序列控制操作可实现的最佳性能来给出操作性基准，包括具有经典或量子前馈的协议。更受限且具有实验动机的控制类别，例如独立酉控制或无记忆量子信道，然后可以与该基准进行比较。我们通过一个两步量子比特纯化任务来说明该框架，在该任务中，最初混合的目标量子比特通过与控制器量子比特的固定相互作用被引导至纯态。该示例展示了简单酉策略饱和高阶基准的机制，以及可证明其次优的机制。这种方法为研究间接量子控制方案中控制资源的价值提供了一种系统途径。

英文摘要

Indirect quantum control aims to manipulate a target system through interventions on an auxiliary controller with which it interacts. We formulate finite-step indirect-control protocols using the language of higher-order quantum operations, representing admissible controller manipulations as deterministic superinstruments. This representation separates the uncontrolled but fixed dynamics from the controllable operations and allows the optimal control problem to be written as a semidefinite program for a chosen figure of merit. The resulting optimum gives an operational benchmark by providing the best performance achievable by a finite sequence of control operations, including protocols with classical or quantum feed-forward. More restricted and experimentally motivated control classes, such as independent unitary controls or memoryless quantum channels, can then be compared against this benchmark. We illustrate the framework with a two-step qubit-purification task, in which an initially mixed target qubit is steered toward a pure state through a fixed interaction with a controller qubit. The example shows regimes where simple unitary strategies saturate the higher-order benchmark, as well as regimes where they are provably suboptimal. This approach provides a systematic way to study the value of control resources in indirect quantum-control schemes.

发表机构

• School of Physical and Mathematical Sciences, Macquarie University（麦考瑞大学物理与数理科学学院）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

12 Pages, 5 Figures